Question

if alpha and beta are zeroes of polynomial ax2+bx+c find the value of 1/alpha square + 1/beta square

Answer 1

Answer:

(b²- 2ac)/ c²

Step-by-step explanation:

Let α and β be the zeroes of the polynomial ax^2 +bx + c

α + β = -b/a

αβ = c/a

Value of 1/α² +  1/β²

= 1/α² +  1/β²

= α² + β² / (αβ)²

{( a + b )² = a² + b² + 2ab

a² + b² = ( a+b )² - 2ab , So α² + β² = -2(αβ) }

=  (α + β)² -2(αβ) / (αβ)²                

=  (-b/a)² - 2(c/a) / (c/a)           { Substitute the value of  (α + β) and (αβ) }          =  (b²/a² - 2c/a) / (c²/a²)

=  [(b²- 2ac)]/a²/ (c²/a²)

(b²- 2ac)/ c²