Question

Find the zeroes of 3x²-5x-2 and verify the relationship between the zeroes and the coefficients. If Alpha=© and Beta=℅

Answer 1

zeros will be 2 and -1/3
sum of Zeroes = -b/a =5/3
product of Zeroes = c/a = 2/3

Answer 2

Given polynomial,

3x²-5x-2 = 0

3x²-6x+x-2=0

3x(x-2)+1(x-2)=0

(x-2)(3x+1)=0

x-2=0 ; 3x+1=0

x=2 ; x=-1/3

Therefore, the zeroes of the polynomial are 2 and -1/3

Let α(alpha) =2
β(beta) =-1/3

Sum of zeroes = α+β=2+(-1/3)
=2-1/3
=(6-1)/3
=5/3=-(-5)/3
=-(x coefficient)/x² coefficient

Product of zeroes=αβ=2(-1/3)=-2/3
=constant/x² coefficient

Hope it helps