Question

Find the zeroes of the quadratic polynomial` (x^2 ˗ 5)` and verify the relation between the zeroes and the coefficients.

Answer 1

We have: 

`f(x) = x^2 ˗ 5` 

It can be written as ` x^2+ o x-5`  

=`(x^2-(sqrt5)^2)` 

=`(x+sqrt5) (x-sqrt5)` 

∴` f(x)=0⇒ (x+sqrt5) (x-sqrt5)=0` 

`⇒ x+sqrt5=0 or x-sqrt5=0` 

`⇒x=-sqrt5 or x=sqrt5` 

So, the zeroes of f(x) are `-sqrt5 and sqrt5` 

Here, the coefficient of x is 0 and the coefficient of `x^2 `is 1. 

Sum of zeroes=-`sqrt5+sqrt5=0/1=-(("Coefficient of x"))/(("Coefficient of "x^2))` 

Product of zeroes`=-sqrt5xxsqrt5=(-5)/1= ("Constant term")/(("Coefficient of" x^2))`