Find the zeros of the polynomial P(x) = 4x²+x and verify their relationship between the zeros and coefficient
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we have,4x^2-1=(2x)^2-(1)^2=(2x-1)(3x+1)
so the value of 4x^2-1 is 0 when either 2x-1=0 or 2x+1=0
I.e.,when x=1/2 or x=-1/2
therefore,zeroes are 1/2,-1/2
Verification of relationship between zeroes and coefficients
sum of zeroes =1/2+(-1/2)=0
-(coffiecient of x)/coffiecient of x^2=0/4=0
Product of zeroes =1/2×-1/2=-1/4
constant term/coffiecient of x^2=-1/4
so the value of 4x^2-1 is 0 when either 2x-1=0 or 2x+1=0
I.e.,when x=1/2 or x=-1/2
therefore,zeroes are 1/2,-1/2
Verification of relationship between zeroes and coefficients
sum of zeroes =1/2+(-1/2)=0
-(coffiecient of x)/coffiecient of x^2=0/4=0
Product of zeroes =1/2×-1/2=-1/4
constant term/coffiecient of x^2=-1/4
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