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If alpha , beta are roots of ax^(3) +b...

If ` alpha , beta` are roots of ` ax^(3) +bx +c=0` then the equation ` ax^(2)-bx(x-1) +c(x-1)^(2)=0` has roots

A

`(alpha)/(1-alpha),(beta)/(1-beta)`

B

`(1-alpha)/(alpha),(1-beta)/(beta)`

C

`(alpha)/(alpha+1),(beta)/(beta+1)`

D

`(alpha+1)/(alpha),(beta+1)/(beta)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
  1. 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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  2. If alpha, beta are the roots of the quadratic equation x^2 + bx - c = ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. If x, y, z are real and distinct, then x^(2) + 4 y^(2) + x + 1 = 0, is

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