Question

if a And b are the zeroes of the quadratic polynomial f(x)=x²-3x-2 then find a²b+ab²​

Answer 1

Given info : if a and b are the zeroes of the quadratic polynomial f(x) = x² - 3x + 2

To find : the value of a²b + b²a

solution : a and b are the zeroes of the quadratic polynomial.

so, sum of zeroes = - coefficient of x/coefficient of x²

⇒a + b = -(-3)/1 = 3 ......(1)

product of zeroes = constant/coefficient of x²

⇒ab = (-2)/1 = - 2......(2)

the value of a²b + b²a

= ab(a + b)

from equations (1) and (2) we get,

= (-2) × 3

= -6

Therefore the value of a²b + b²a = -6