Question

show that 1\2 and -3\2 are 2 zeros of polynomial 4x²+4x-3 and verify relarion btn 0s and coefficient's of polynomial.

Answer 1

Let p(x)=4x^2+4x-3
i)p(1/2)=4×(1/2)^2+4*1/2 -3
=1+2-3=0
p(1/2)=0---(1)
ii)p(-3/2)=4*(-3/2)^2+4*(-3/2)-3
=9-6-3
=0
p(-3/2)=0---(2)
From (1) and (2) we conclude that
1/2 and -3/2 are two zeroes of p(x)

iii) compare given equation with ax^2+bx+c=0
a= 4, b=4, c=-3
i) sum of the roots = -b/a=-(4/4)= -1
From given zeroes
Sum =1/2-3/2=-2/2= -1

ii) product of the zeroes=c/a=-3/4
By given zeroes
Product = 1/2*(-3/2)=-3/4