Question

find the zeros of each of the following polynomial and verify the relation between zeros and their coficients. f¹(x)= x²-2x-8

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Answer 1

x^2-2x-8=0

by splitting middle term method

x^2-4x+2x-8=0

x(x-4)+2(x-4)=0

(x-4)(x+2)=0

x-4=0, x =4

x+2 , x =-2

Let alpha=4 and bita =-2

On comparing x^2-2x-8 to ax^2+bx+c

a = 1 , b= -2 , c=-8

sum of zero= -b/a

alpha +bita = -(-2)/1

4+-2=2

2=2 , LHS = RHS

product of zero= c/a

alpha×bita = -8/1

4×-2 = -8

-8=-8, LHS= RHS

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