Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

$2x^2-11x+15$

Answer 1

We have

f(x) = 2x^2 – 11x + 15

= 2x^2 – 6x – 5x + 15

= 2x(x – 3) – 5(x – 3) = (x – 3)(2x – 5)

Now, f(x) = (x – 3)(2x – 5) = 0

Therefore, x – 3 = 0 or 2x – 5 = 0

⇒⇒ x = 3 or x = 5/2

So zeros of f(x) are 3 and 5/2

Sum of zeros = 3+5/2=11/2= -(−11)/2=−Coeff.of x/Coeff.of x^2

Product of zeros = 3×5/2=15/2=Constant term/Coeff.ofx^2