Question

If a and Bare the zeros of the quadratic polynomial p(x) = 4x2 - 5x - 1, find the value
1.a^2b+ab^2​

Answer 1

Answer:

given Eqn is 4x²-5x-1

here comparing with ax²+bx+c so a=+4 b=-5 c=-1

$now product of roots =ab= \frac{c}{a} = \frac{ - 1}{4}$

$sum \: of \: roots =a + b = \frac{ - b}{a} = \frac{ - ( - 5)}{4} = \frac{5}{4}$

$</strong><strong>a²b+ab²=ab(a+b) \\ =( \frac{ - 1}{4} )( \frac{5}{4} ) = \frac{ - 5}{16}$