Question

if alpha, beta are the zeroes of ax^2+bx+c, then find 1/alpha^2+1/beta^2

Answer 1

Answer :

The polynomial is (ax² + bx + c).

Since, α and β are the zeroes of this polynomial,

α + β = -b/a ...(i)

and

αβ = c/a ...(ii)

Now,

1/α² + 1/β²

= (β² + α²)/(α²β²)

= {(α + β)² - 2αβ}/(αβ)²

= {(-b/a)² - 2(c/a)}/(c/a)², by (i) and (ii)

= (b²/a² - 2c/a)/(c²/a²)

= {(b² - 2ca)/a²}/(c²/a²)

= (b² - 2ca)/c²

#MarkAsBrainliest