Question

If α and β are the zeroes of the polynomial ax^2+ bx +c then find
(a) α/β+ β/α
(b) α^2+β ^2
please answer ​

Answer 1

Step-by-step explanation:

alpha + beta = -b/a

alpha * beta = c/a

(a) alpha/beta + beta/alpha

= (alpha ² + beta²)/alpha*beta

= {(alpha + beta)² - 2alpha*beta}/alpha*beta

= { (-b/a)² - 2(c/a)} / (c/a)

= { (b²/a²) - (2c/a) } / (c/a)

= { (b² - 2ac)/a² } / (c/a)

= (b²-2ac)/ac

(b) alpha² + beta²

(alpha+beta)² - 2alpha*beta

(-b/a)² - 2(c/a)

(b²/a²) - (2c/a)

(b² - 2ac)/a²