11x1 t10 07 sum and product of roots (2010)
TRANSCRIPT
![Page 1: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/1.jpg)
Sum and Product of Roots
![Page 2: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/2.jpg)
Sum and Product of Roots2If and are the roots of 0, then;ax bx c
![Page 3: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/3.jpg)
Sum and Product of Roots2If and are the roots of 0, then;ax bx c
2ax bx c a x x
![Page 4: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/4.jpg)
Sum and Product of Roots2If and are the roots of 0, then;ax bx c
2ax bx c a x x
2 2ax bx c a x x x
![Page 5: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/5.jpg)
Sum and Product of Roots2If and are the roots of 0, then;ax bx c
2ax bx c a x x
2 2ax bx c a x x x
2 2b cx x x xa a
![Page 6: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/6.jpg)
Sum and Product of Roots2If and are the roots of 0, then;ax bx c
2ax bx c a x x
2 2ax bx c a x x x
2 2b cx x x xa a
Thus
![Page 7: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/7.jpg)
Sum and Product of Roots2If and are the roots of 0, then;ax bx c
2ax bx c a x x
2 2ax bx c a x x x
2 2b cx x x xa a
Thus (sum of roots)b
a
![Page 8: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/8.jpg)
Sum and Product of Roots2If and are the roots of 0, then;ax bx c
2ax bx c a x x
2 2ax bx c a x x x
2 2b cx x x xa a
Thus (sum of roots)b
a
(product of roots)ca
![Page 9: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/9.jpg)
e.g. (i) Form a quadratic equation whose roots are;
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e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
![Page 11: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/11.jpg)
e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1
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e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
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e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
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e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
) 2 5 and 2 5b
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e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
) 2 5 and 2 5b 4
![Page 16: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/16.jpg)
e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
) 2 5 and 2 5b 4 4 5
1
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e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
) 2 5 and 2 5b 4 4 5
1
2 4 1 0x x
![Page 18: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/18.jpg)
e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
) 2 5 and 2 5b 4 4 5
1
2 4 1 0x x
2( ) If and are the roots of 2 3 1 0, find;ii x x
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e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
) 2 5 and 2 5b 4 4 5
1
2 4 1 0x x
2( ) If and are the roots of 2 3 1 0, find;ii x x
) a
![Page 20: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/20.jpg)
e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
) 2 5 and 2 5b 4 4 5
1
2 4 1 0x x
2( ) If and are the roots of 2 3 1 0, find;ii x x
) a
32
ba
![Page 21: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/21.jpg)
e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
) 2 5 and 2 5b 4 4 5
1
2 4 1 0x x
2( ) If and are the roots of 2 3 1 0, find;ii x x
) a
32
ba
) b
![Page 22: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/22.jpg)
e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a
1 6
2 6 0x x
) 2 5 and 2 5b 4 4 5
1
2 4 1 0x x
2( ) If and are the roots of 2 3 1 0, find;ii x x
) a
32
ba
) b
12
ca
![Page 23: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/23.jpg)
2 2) c
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2 2) c 2 2
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2 2) c 2 2 23 12
2 2
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2 2) c 2 2 23 12
2 2
9 14134
![Page 27: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/27.jpg)
2 2) c 2 2 23 12
2 2
9 14134
1 1) d
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2 2) c 2 2 23 12
2 2
9 14134
1 1) d
![Page 29: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/29.jpg)
2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
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2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
3
![Page 31: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/31.jpg)
2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
3
2( ) Find the value of if one root is double the other in 6 0iii m x x m
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2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
3
2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2
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2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
3
2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2
2 6
![Page 34: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/34.jpg)
2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
3
2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2
2 6
3 62
![Page 35: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/35.jpg)
2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
3
2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2
2 6 2 m
3 62
![Page 36: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/36.jpg)
2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
3
2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2
2 6 2 m
3 62
22 m
![Page 37: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/37.jpg)
2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
3
2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2
2 6 2 m
3 62
22 m 22 2 m
![Page 38: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/38.jpg)
2 2) c 2 2 23 12
2 2
9 14134
1 1) d
321
2
3
2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2
2 6 2 m
3 62
22 m 22 2 m
8m
![Page 39: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/39.jpg)
2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x
![Page 40: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/40.jpg)
2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x
1Let the roots be and
![Page 41: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/41.jpg)
2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x
1Let the roots be and
1 12 1m
![Page 42: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/42.jpg)
2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x
1Let the roots be and
1 12 1m
112 1m
![Page 43: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/43.jpg)
2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x
1Let the roots be and
1 12 1m
112 1m
2 1 12 2
1
mmm
![Page 44: 11X1 T10 07 sum and product of roots (2010)](https://reader033.vdocument.in/reader033/viewer/2022060120/5591a21a1a28ab9a268b4765/html5/thumbnails/44.jpg)
2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x
1Let the roots be and
1 12 1m
112 1m
Exercise 8H; 3beh, 4bdf, 5, 6, 7abc i, 8, 10, 12,13cd, 15, 18, 20, 21ac
2 1 12 2
1
mmm