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If alpha, beta are the roots of the quad...

If `alpha, beta` are the roots of the quadratic equation `x^2 + bx - c = 0`, the equation whose roots are `b` and `c`, is a. `x^(2)+alpha x- beta=0` b. `x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0` c. `x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0` d. `x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0`

A

`x^(2) + alpha x - beta = 0`

B

`x^(2) -x(alpha +beta + alpha beta) - alpha beta(alpha + beta) = 0`

C

`x^(2) + (alpha + beta - alpha beta) x - alpha beta (alpha+beta) = 0`

D

`x^(2) + x(alpha + beta + alpha beta) + alpha beta(alpha + beta) = 0`

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
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  2. If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0...

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  3. If alpha, beta are the roots of the quadratic equation x^2 + bx - c = ...

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  4. If alpha , beta are roots of ax^(3) +bx +c=0 then the equation ax^...

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  5. If alpha ne beta but alpha^(2)= 5 alpha - 3 and beta ^(2)= 5 beta...

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  6. The expression y = ax^2+ bx + c has always the same sign as of a if (A...

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  7. If alpha,betaa n dgamma are the roots of x^2+8=0 then find the equatio...

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  8. Given that a x^2+b x+c=0 has no real roots and a+b+c<0, then c!=0 b. c...

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  9. If x in R, then the expression 9^(x) - 3^(x) + 1 assumes

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  10. The values of 'a' for which the roots of the equation x^(2) + x + a = ...

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  11. Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation wh...

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  12. The roots alpha, beta and gamma of an equation x^(3) - 3 a x^(2) + 3 b...

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  13. If b and c are odd integers, then the equation x^2 + bx + c = 0 has-

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  14. If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roo...

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  15. If both the roots of the equation ax^(2) + bx + c = 0 are zero, then

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  16. If alpha, beta , gamma, delta are the roots of the equation x^4+x^2+1=...

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  17. The number of real roots of (x+1/x)^3+x+1/x=0 is

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  18. The roots of the equation (3 - x)^(4) + (2 - x)^(4) = (5 - 2x)^(4) are

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  19. The real roots of the equation |x|^3-3x^2+3|x|-2=0 are

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  20. The number of positive integral roots of x^(4) + x^(3) - 4 x^(2) + x +...

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