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Question

Find the zeroes of the quadratic polynomial 4x2-4x-3 and verify the relationship between the zeroes and the coefficients of the polynomial.


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Solution

Step 1: Form the equation

The given polynomial is 4x2-4x-3

We know that the zeroes of a polynomial are evaluated by equating them with zero.

px=0

4x2-4x-3=0

Step 2: Solve to find the zeroes

4x2-4x-3=0

4x2-6x+2x-3=0

2x2x-3+12x-3=0

2x-32x+1=0

x=32,-12

Step 3: Verification

We know that for a given polynomial ax2+bx+c,

Sum of the zeroes=-ba and product of the roots=ca

Sum of the zeroes =32-12=1

Again, -ba=44=1

Product of the zeroes =32×-12=-34

Again, ca=-34

Thus, the relationship between the zeroes and the coefficients of the polynomial is verified.

Hence, the zeroes of this polynomial are 32 and -12.


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