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Formation of a Quadratic Equation From It's Roots

If α, β are t...

Question

If α, β are the zeros of the polynomial f(x) = ax² + bx + c, then $\frac{1}{α^{2}} + \frac{1}{β^{2}} =$

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

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Solution

We have to find the value of

Given and are the zeros of the quadratic polynomial f(x)

We have,

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}}

Q. 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}}

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

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

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

Q. If the roots of

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

α, β

and the roots of

A X^{2} + B x + C = 0

(α - k), (β - k)

(\frac{B^{2} - 4 A C}{b^{2} - 4 a c})

α

β

be the zeros of

f (x) = a x^{2} + b x + c, a \neq 0

Δ = b^{2} - 4 a c

α + β, α^{2} + β^{2}

α^{3} + β^{3}

are in G.P., then :

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}})

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Formation of a Quadratic Equation From It's Roots

Standard X Mathematics

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