MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

Open in App

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

Suggest Corrections

thumbs-up

0

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}})

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Formation of a Quadratic Equation From It's Roots

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon