Question

Find the zeroes of the quadratic polynomial x² + 7x + 10 and verify the relationship between the zeroes and the coefficients.

Answer 1

Let p(x) = x² + 7x + 10

For zeroes of polynomial put p(x) = 0.

∴ x² + 7x + 10 = 0

x² + 5x + 2x + 10 = 0

x(x + 5) + 2(x + 5) = 0

(x + 5) (x + 2) = 0

So, x = –2, –5

Therefore, α = –2 and β = –5 are the zeroes of the given polynomial.

Verification:

Sum of zeroes = α + β

= –2 + (–5)

= –7

= `(-7)/1`

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

Product of zeores = αβ

= (–2)(–5)

= 10

= `10/1`

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

Hence Verified.