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Find the condition which must be satisfi...

Find the condition which must be satisfied by the zeros of `f(x) = x^(3) - px^(2) + qx - r` , when the sum of its two zeros is zero .

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The correct Answer is:
pq = r is the required consdition.
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ZEN PUBLICATION-POLYNOMIALS-ZEN ADDITIONAL QUESTIONS ( Short answer [SA] type I questions )
  1. If alpha and beta are zeros of x^(2) - 2x + 3, find a polynomial who...

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  2. If two zeros of a polynomial p(x) = x^(3) - 4x^(2) - 3x + 12 " are " s...

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  3. Find the condition which must be satisfied by the zeros of f(x) = x^(3...

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  4. (i) Verify that the numbers given alongside of the cubic polynomials b...

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  5. If alpha and beta are zeros of polynomial 2x^(2) + 7 x + 5 " find " al...

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  6. If alpha and beta are zeros of p(x) = 4x^(2) + 3x + 7 , "find" (1)/(a...

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  7. If one zero of f(x) = (k^(2) +4) x^(2) + 13x + 4k is the reciprocal of...

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  8. If alpha , beta, and gamma are the zeroa od f(x) = ax^(3) + bx^(2) +c...

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  9. If alpha, beta, and gamma are the zeros of 2x^(3) - 4x^(2) + 6x +9, fi...

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  10. If zeros of a quadratic polynomial x^(2) + (a +1) x + b are 2 and -3, ...

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  11. Find zeros of polynomials by the algebraic method and verify the relat...

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  12. Given f(x+1) = 3x +5 , evaluate f(-2) and f(x)

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  13. If the product of the zeros of a polynomial (ax^(2) - 6x - 6) is 4, fi...

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  14. If alpha and beta are the zeros of the quadratic polynomial 4x^(2) + 4...

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  15. Find values of p for which the quadratic polynomial 4x^(2) + px +3 h...

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  16. Find a if one zero of (a^(2) +9) x^(2) + 13x + 6a is a reciprocal of...

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  17. If two zeros of f(x) = x^(3) - 4x^(2) - 3x + 12 are sqrt(3) and - sqrt...

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  18. Without solving, find the value of m for which the zeros are equal fo...

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  19. Find values of k for which (k +4) x^(2) + (k +1) x+1 has equal zeros.

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  20. The sum and product of the zeroes an a quadratic polynomial P (x) = ax...

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