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If alpha, beta, gamma be the zeros of th...

If `alpha, beta, gamma` be the zeros of the polynomial p(x) such that `(alpha+beta+gamma) = 3, (alpha beta+beta gamma+gamma alpha) =- 10 and alpha beta gamma =- 24 ` then p(x) = ?

A

`x^(3)+3x^(2)-10x+24`

B

`x^(3)+3x^(2)+10x-24`

C

` x^(3) - 3x^(2) - 10x + 24`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
` p(x) = x^(3) -(alpha+beta+gamma) x^(2) + (alpha beta+beta gamma+gamma alpha) x - alpha beta gamma`
` = x^(3) - 3x^(2) - 10x + 24.`
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RS AGGARWAL-POLYNOMIALS-Multiple Choice Questions (Mcq)
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  8. If -2 and 3 are the zeros of the quadratic polynomial x^(2) + (a+1) ...

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  9. If one zero of 3x^(2) + 8x + k be the reciprocal of the other then k...

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  13. If alpha, beta, gamma are the zeros of the polynomial 2x^(3)+ x^(2) ...

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  14. If alpha, beta, gamma be the zeros of the polynomial p(x) such that (...

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  15. If two of the zeros of the cubic polynomial ax^(3)+bx^(2)+cx+d are 0 t...

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  17. If one of the zeroes of the cubic polynomial x^3 + ax^2 + bx + c is -1...

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  18. If alpha, beta be the zeros of the polynomial 2x^(2)+5x+k such that...

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  19. On dividing a polynomial p(x) by a non-zero polynomial q(x), let g(x)...

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  20. Which of the following is a true statement ?

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