Question

Find the zeroes of the quadratic polynomial 2x² – 11x + 15 and verify the relation between the zeroes and the coefficients.

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

2x² – 11x + 15

Answer 1

f(x) = 2x² – 11x + 15

= 2x² – (6x + 5x) + 15

= 2x² – 6x – 5x + 15

= 2x(x – 3) – 5(x – 3)

= (2x – 5) (x – 3)

∴ f(x) = 0 ⇒ (2x – 5) (x – 3) = 0

⇒ 2x – 5 = 0 or x – 3 = 0 

⇒ `x = 5/2` or x = 3 

So, the zeroes of f(x) are `5/2` and 3. 

Sum of zeroes = `5/2 + 3`

= `(5 + 6)/2`

= `11/2`

= `(-("Coefficient of x"))/(("Coefficient of"  x^2))` 

Product of zeroes = `5/2 xx 3`

= `(-15)/2`

= `("Constant term")/(("Coefficient of"  x^2))`