Question

Find the zeroes of the quadratic polynomial f(x) = x² + 3x – 10 and verify the relation between its zeroes and coefficients.

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

x² + 3x – 10

Answer 1

We have:

f(x) = x² + 3x – 10

= x² + 5x – 2x – 10

= x(x + 5) – 2(x + 5)

= (x – 2) (x + 5)

∴ f(x) = 0 ⇒ (x – 2) (x + 5) = 0

⇒ x – 2 = 0 or x + 5 = 0

⇒ x = 2 or x = –5.

So, the zeroes of f(x) are 2 and –5.  

Sum of zeroes = 2 + (–5)

= –3

= `(-3)/1`

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

 Product of zeroes = 2 × (–5)

= –10

= `(-10)/1`

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