Question

 If α and β are zeros of a quadratic polynomial x2 -6x +y. Find the value of y , if 3α + 2β = 20 ​

Answer 1

If α and β are the zeros of the polynomial then

(x−α)(x−β) are the factors of the polynomial

Thus, (x−α)(x−β) is the polynomial.

So, the polynomial =x

2

−αx−βx+αβ

=x

2

−(α+β)x+αβ....(i)

Now,the quadratic polynomial is

2−3x−x

2

= x

2

+3x−2....(ii)

Now, comparing equation (i) and (ii),we get,

−(α+β)=3

α+β=−3