Question

Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1. Hence, find the zeroes of the polynomial. 

Answer 1

Let 𝛼 and 𝛽 be the zeroes of the required polynomial f(x). 

Then (𝛼 + 𝛽) = 0 and 𝛼𝛽 = -1 

`∴ F(x)=x^2-(∝+β)x+∝β ` 

⇒ `f(x)=x^2-o x+(-1)` 

⇒`f(x) = x2 ˗ 1` 

Hence, required polynomial `f(x) =x^2-1` 

`∴ f(x)=0⇒ x^2-1=0` 

         `⇒ (x+1) (x-1)=0` 

        `⇒(x+1)=0 or (x-1)=0` 

      ` ⇒ x=-1 or x=1`  

So, the zeroes of f(x) are -1 and 1.