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Formation of a Quadratic Equation From It's Roots

If α, β, γ ar...

Question

If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx²+ cx + d, then α² + β² + γ² =

(a) $\frac{b^{2} - a c}{a^{2}}$
(b) $\frac{b^{2} - 2 a c}{a}$
(c) $\frac{b^{2} + 2 a c}{b^{2}}$
(d) $\frac{b^{2} - 2 a c}{a^{2}}$

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Solution

We have to find the value of

Given be the zeros of the polynomial

Now

The value of

Hence, the correct choice is

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Similar questions

Q. If α, β are the zeros of the polynomial ax² + bx + c, then (α² + β²) = ?

(a)

\frac{a^{2} - 2 b c}{b^{2}}

\frac{b^{2} - 2 a c}{a^{2}}

\frac{a^{2} + 2 b c}{b^{2}}

\frac{b^{2} + 2 a c}{a^{2}}

α

β

are the roots of the equation

a x^{2} + b x + c = 0

then the equation whose roots are

(α^{2} + β^{2}), (\frac{1}{α^{2}} + \frac{1}{β^{2}})

Q. If α, β are the zeros of the polynomial f(x) = ax² + bx + c, then

\frac{1}{α^{2}} + \frac{1}{β^{2}} =

\frac{b^{2} - 2 a c}{a^{2}}

\frac{b^{2} - 2 a c}{c^{2}}

\frac{b^{2} + 2 a c}{a^{2}}

\frac{b^{2} + 2 a c}{c^{2}}

α, β, γ

are zeros of the polynomial

a x^{3} + b x^{2} + c x + d

α β γ =

α, β, γ

are the zeroes of the cubic polynomial

a x^{3} + b x^{2} + c x + d = 0

α + β + γ = \frac{- b}{a}

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Formation of a Quadratic Equation From It's Roots

Standard X Mathematics

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