Question

If alpha, beta are the roots of ax²+bx+c=0, then 1\alpha²+1\beta² is​

Answer 1

Answer:

(b² - 2ac)/c²

Step-by-step explanation:

Equation : ax² + bx + c = 0 ; Roots = α and β

Sum of roots = α+β = -b/a

Product of roots αβ = c/a

now

1/α² + 1/β² = (α²+β²)/ (αβ)²

= [(α+β)² - 2αβ ]/(αβ)²

Putting values of α+β and αβ we get

[(α+β)² - 2αβ ]/(αβ)² = [(-b/a)² - 2(c/a)]/(c/a)²

upon simplification : (b² - 2ac)/c²

Answer 2

Step-by-step explanation:

GIVEN :

If alpha, beta are the roots of ax²+bx+c=0, then 1\alpha²+1\beta² is

to find :

then 1\alpha²+1\beta² is

solution :

• the answer is b/ac

• hope it helps you