Question

If alpha and beta are the zeroes of the polynomial ax2+bx+c.find the value of alpha2+beta2​

Answer 1

Answer:

ax² + bx + c = 0

Required value : α² - β²

α + β ( α - β )

Sum of roots : α + β = - b / a

Difference of roots : α - β = √D/ a

D = Discriminant = b² - 4ac

Hence , Required value :

- b √D / a²

Step-by-step explanation:

Answer 2

Step-by-step explanation:

alpha + beta = -b/a

alpha beta = c/a

alpha² + beta²

= (alpha + beta)² - 2alpha*beta

= (-b/a)² - 2(c/a)

= (b²/a²) - 2c/a

= (b²-2ac)/a²