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If alpha,beta are roots of x^2+-p x+1=0a...

If `alpha,beta` are roots of `x^2+-p x+1=0a n dgamma,delta` are the roots of `x^2+q x+1=0` , then prove that `q^2-p^2=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta)` .

A

`p^(2) - q^(2)`

B

`q^(2) - p^(2)`

C

`p^(2)`

D

`q^(2)`

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Chapter Test
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  3. Let [x] denote the greatest integer less than or equal to x. Then, int...

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  5. Find the value of a for which one root of the quadratic equation (a^2-...

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  6. If alpha, beta, gamma are the roots of the equation x^(3) + ax^(2) + b...

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  7. If alpha,beta and gamma are the roots of x^3+qx + r = 0 thensumalpha/(...

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  8. If alpha, beta are the roots of the equation ax^2 + bx +c=0 then the v...

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  9. If alpha,beta are roots of x^2+-p x+1=0a n dgamma,delta are the roots ...

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  10. The maximum number of real roots of the equation x^(2n) -1 = 0, is

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  11. The integral value of k for which the roots of the equation (x-2)x^(...

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  12. If x^(2//3) -7 x^(1//3) + 10 = 0, then the set of values of x, is

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  13. If x^2+2ax+10-3a gt0 for all x in R then

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  14. If the difference between the corresponding roots of x^(2)+ax+b=0and x...

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  15. Product of real roots of the equation t^2x^2+|x|+9=0 a. is always +ve...

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  16. Find the value of a for which the sum of the squares of the roots of t...

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  17. If x^(2)+ax+10=0and x^(2)+bx-10=0 have common root, then a^(2)-b^(2) i...

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  18. If x^2+p x+q=0 is the quadratic equation whose roots are a-2a n d b-2 ...

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  19. If alpha and beta are the roots of the equation x^(2)-ax+b=0and A(n)=a...

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  20. If the equation ax^(2)+bx+c=0(agt0) has two roots alpha and beta such ...

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