Question

9-If α and β are the zeroes of the polynomial P(x)= 2x²+11x-3, then the value of α²+β² is *

Answer 1

Answer:

α²+β² = 33.25

Step-by-step explanation:

P(x)= 2x²+11x-3

compare with ax²+bx+c

a = 2, b = 11, c = -3

α and β are the zeroes ( roots) of P(x)

sum of the two zeroes are

α + β = - b / a = - 11/2

product of the two zeroes are

α * β = c / a = -3/2

now, α²+β² = ( α + β )² - 2 α * β

= ( - 11/2)² - 2 ( -3/2)

= ( 121/4) + 3

= 30.25 + 3

α²+β² = 33.25