Question

if alpha beta are the zeros of the quadratic polynomial ax^2+bx+c, a not equal to 0 ,then prove that a(x-alpha)(x-beta) is equal to ax^2+bx+c​

Answer 1

Answer:

If α and β are the zeroes of the quadratic polynomial, then

aα

2

+bα+c=0 and

aβ

2

+bβ+c=0

or, aα

2

+bα − aβ

2

−bβ=0

Then, α+β=

a

−b

and αβ=

ab

c