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if one zero of the quadratic polynomial 4xsquare + 5x+ gama be reciprocal of another zero, find the value of gama.

  • maths -

    Equate coefficients of terms:
    for x²: 4=4
    for x: -4(k+1/k)=5
    for constant term: γ=1

    So the equation is:

  • maths -

    let the roots be p and 1/p

    We know that for ax^2 + bx + c = 0
    the sum of the roots = -b/a
    product of roots = c/a

    so in our case, product of the roots = gamma/4
    but the product of roots = p(1/p) = 1
    gamma/4 = 1

    gamma = 4

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