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If alpha, beta are the roots of the equa...

If `alpha, beta` are the roots of the equation `ax^(2)+bx+c=0`, find the value `(1)/(alpha^(2))+(1)/(beta^(2))` expressions in terms of a,b,c.

Text Solution

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The correct Answer is:
`=(b^(2)-2ac)/(c^(2))`
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If alpha, beta are the roots of the equation ax ^(2) + bx + c =0, then find the value of (1)/(alpha ^(2)) + (1)/(beta ^(2)).

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Knowledge Check

  • If alpha, beta, gamma are the roots of the equation x^(3) - ax^(2) + bx -c = 0 , then sum alpha^(2) (beta + gamma)=

    A
    ab - 3c
    B
    `(ab - 3c)/(c )`
    C
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    D
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  • If alpha, beta are the zeros of the polynomial f(x) = ax^(2) + bx + c then 1/(alpha^2) + 1/(beta^2) = …………….

    A
    `b^(2) -2ac`
    B
    `(b-4ac)/(c )`
    C
    `(b-4ac)/(c^2)`
    D
    `(b^(2) -2ac)/(c^2)`

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