Question

8. If α and β are the zeroes of the quadratic polynomial p(x) = 4x2 – 5x +1, then find the value of α2β + β2α​

Answer 1

Step-by-step explanation:

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Answer 2

α²β+αβ²=αβ(α+β)=(-1/4)(5/4)=-5/16

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 is 4x²-5x-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