Question

Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. 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) = 8 and 𝛼𝛽 = 12 

∴ `f(x)=x^2-(∝+β)x+∝β ` 

`⇒ f(x)=x^2-8x+12` 

Hence, required polynomial `f(x)=x^2-8x+12`  

`∴ f(x)=0 ⇒ x^2-8x+12=0` 

`⇒ x^2-(6x+2x)+12=0`  

`⇒ x^2-6x-2x+12=0`

`⇒x(x-6)-2(x-6)=0` 

`⇒ (x-2) (x-6)=0` 

`⇒ (x-2)=0 or (x-6)=0` 

`⇒x=2 or x=6` 

So, the zeroes of f(x) are 2 and 6.