Question

IF α AND β ARE THE ZEROES OF THE POLYNOMIAL p(x)=4x²-5x-1, find the value of α²β+αβ².

Answer 1

α²β+αβ²=αβ(α+β)=(-1/4)(5/4)=-5/16
explanation:
if the quadratic equation is in the form
ax²+bx+c=0
then SUM OF ROOTS=-b/a
and product of roots=c/a
so if the equation is4x²-5x-1
then a=4,b=-5,c=-1
so sum of roots=α+β=5/4
then product of roots=αβ=-1/4
so α²β+αβ²=αβ(α+β)=(-1/4)(5/4)=-5/16

Answer 2

5/16 is your answer hope this helps!!