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If alpha, beta, gamma are the roots of t...

If `alpha, beta, gamma` are the roots of the equation `x^3 + px^2 + qx + r = 0,` then the value of `(alpha - 1/(beta gamma))(beta - 1/(gamma alpha))(gamma - 1/(alpha beta))` is

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The correct Answer is:
`-((r+1)^(3))/(r^(2))`
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MOTION-QUADRATIC EQUATION-EXERCISE -3 (SUBJECTIVE)
  1. If the quadratic equations x^2+bx+ca=0 & x^2+cx+ab=0 (where a!= 0) ha...

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  2. Solve the equation x^4 + 4x^3 + 5x^2 + 2x-2=0, one root being -1+sqrt...

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  3. If alpha, beta, gamma are the roots of the equation x^3 + px^2 + qx + ...

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  4. If alpha,betaa n dgamma are roots of 2x 63+x^3-7=0 , then find the val...

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  5. Let alpha+ibeta,alpha, beta epsilon R, be a root of the equation x^(3)...

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  6. Let alpha,beta,gamma are the roots of the cubic x^3-3x^2+1=0 .Find a c...

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  7. Two roots of a biquadratic x^4-18x^3+ kx^2+ 200x-1984=0 have their pro...

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  8. Suppose a cubic polynomial f(x) = x^3 + px^2 + qx + 72 is divisible by...

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  9. If g(x)=x^(3)+px^(2)+qx+r where p,q,r are integers. If g(0) and g(-1)...

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  10. If x be real then find the range of the following rational expressions...

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  11. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

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  12. Find the range of values of a, such that f(x)=(ax^2+2(a+1)x+9a+4)/(x^2...

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  13. The least value of the quadratic polynomial, f(x) = (2p^(2) + 1) x^(2)...

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  14. Find all real numbers x such that (x-1/x)^(1/2)+(1-1/x)^(1/2)=x

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  15. The minimum value of ((x+1/x)^6-(x^6+1/(x^6))- 2)/((x+1/x)^3+x^3+1/x^...

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  16. Find the product of the real roots of the equation, x^2+18x +30=2sqrt(...

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  17. The values of b for which the equation 2log(1/25)(bx+28)=1log5(12-4x-x...

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  18. Find all the values of the parameters c for which the inequality has a...

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  19. Find the complete set of real values of a for which both roots of the ...

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  20. Let p(x) = x^2+bx+c, where b and c are integers. If p(x) is a factor o...

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