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Formation of a Quadratic Equation From It's Roots

Find the cond...

Question

Find the condition that the zeros of the polynomial f(x) = x³ + 3px² + 3qx + r may be in A.P.

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Solution

Let and be the zeros of the polynomials .Then,

Sum of the zeros =

Since is a zero of the polynomial .Therefore,

Substituting we get,

Hence, the condition for the given polynomial is .

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Formation of a Quadratic Equation From It's Roots

Standard X Mathematics

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