Linear and Quadralic Equations and Inequalities.
Prove that the roots of the quadratic equations $a x^{2} + b x + c = 0 a n d c x^{2} + b x + a = 0$ are mutually inverse.

Open in App

Solution

in the first equation let roots be $x, y$

now if we substitute $\frac{1}{x}$ and $\frac{1}{y}$ in equation $1$

by soving we get equation 2 therefore the roots of the first equation are mutually inverse

Suggest Corrections

Similar questions

a x^{2} + b x + c ϵ Z f o r a l l x ϵ Z t h e n a, b, c, ϵ Z .

a x^{2} - b x + c

x_{1} 0, x_{2} = 1, a n d x_{3} = 2,

Zeroes of the quadratic polynomial ax² + bx + c and roots of the quadratic equation ax² + bx + c = 0 are__________

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

c = 0

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

Join BYJU'S Learning Program