Question

Find the zeroes of the quadratic polynomial f(x) = 5x² – 4 – 8x and verify the relationship between the zeroes and coefficients of the given polynomial.

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

5x² – 4 – 8x

Answer 1

We have:

f(x) = 5x² – 4 – 8x

= 5x² – 8x – 4

= 5x² – (10x – 2x) – 4

= 5x² – 10x + 2x – 4

= 5x(x – 2) + 2(x – 2)

= (5x + 2) (x – 2)

∴ f(x) = 0 ⇒ (5x + 2) (x – 2) = 0 

⇒ 5x + 2 = 0 or x – 2 = 0

⇒ `x = (-2)/5` or x = 2 

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

Sum of zeroes =`((-2)/5) + 2`

= `(-2 + 10)/5`

= `8/5`

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

Product of zeroes = `((-2)/5) xx 2`

= `(-4)/5`

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