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Suppose a cubic polynomial f(x) = x^3 + ...

Suppose a cubic polynomial `f(x) = x^3 + px^2 + qx + 72` is divisible by both `x^2 + ax + b` and `x^2+ bx +a` (where a, b, p, q are constants and `a!=b`). Find the sum of the squares of the roots of the cubic polynomial.

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MOTION-QUADRATIC EQUATION-EXERCISE -3 (SUBJECTIVE)
  1. Let alpha,beta,gamma are the roots of the cubic x^3-3x^2+1=0 .Find a c...

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

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

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

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

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

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

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

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

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

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

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

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  16. Find the value of k for which one root of the equation of x^(2)-(k+1)x...

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  17. If the roots of x^2-ax+b=0 are real and differ by a quantity which is ...

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  18. If alpha, beta are the roots of the equation x^(2)-2x-a^(2)+1=0 and ga...

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  19. Find the values of k so that the quadratic equation x^2+2(k-1)x+k+5=0 ...

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  20. If the equation has four real and distinct roots, then lamda lies in t...

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