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If alpha and beta are the zeros of the q...

If `alpha and beta` are the zeros of the quadratic polynomial `4x^(2) + 4x +1` ,find the quadratic polynomial whose zeros are `2 alpha and 2 beta` .

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The correct Answer is:
`x^(2) + 2x + 1`
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ZEN PUBLICATION-POLYNOMIALS-ZEN ADDITIONAL QUESTIONS ( Short answer [SA] type I questions )
  1. If alpha and beta are zeros of p(x) = 4x^(2) + 3x + 7 , "find" (1)/(a...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Find the quotient and the remainder when P (x) = 3x^(3)+ x^(2)+2x+5 is...

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  17. Sum and product of the zeroes of a quadratic polynomial P(x) = ax^(2)...

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  18. Find the value of k of polynomial P(x) = x^(2) - x - (2k +2) in whic...

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  19. If one zero of the polynomial p(x) = x^(2) - 6x + k is twice the other...

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  20. Find the polynomial of least degree that should be subtracted from p(x...

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