Question

Solve :-1/alpha square + 1/beta square.IF alpha and beta are the roots of the quadratic equation ax^2+bx+c=0

Answer 1

Answer:

Value of $\frac{1}{\alpha}+\frac{1}{\beta}\:\:is\:\:\frac{-b}{c}$

Step-by-step explanation:

Given: Quadratic Equation, ax² + bx + c = 0

           α and β are roots

To find: $\frac{1}{\alpha}+\frac{1}{\beta}$

We know that sum of zeroes/roots = $\frac{-coefficient\:of\:x}{coefficient\:of\:x^2}$

and Product of zeroes/roots = $\frac{constant\:term}{coefficient\:of\:x^2}$

⇒ $\alpha+\beta=\frac{-b}{a}$  and $\alpha\beta=\frac{c}{a}$

Consider,

$\frac{1}{\alpha}+\frac{1}{\beta}$

$\implies\frac{\beta+\alpha}{\alpha\beta}$

$\implies\frac{\frac{-b}{a}}{\frac{c}{a}}$

$\implies\frac{-b}{c}$

Therefore, Value of  $\frac{1}{\alpha}+\frac{1}{\beta}\:\:is\:\:\frac{-b}{c}$

Answer 2

Answer:

if 2 and -3 of zeros of quadratic polynomial X square + A + 1 X + b then find the value of a and b