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Question

Find the zeros of the following quadratic polynomials x2-1 and verify the relationship between the zeros and the coefficients.


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Solution

Step 1: Form the equation

The given polynomial is x2-1=x2+0.x-1.

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

px=0

x2-1=0

Step 2: Solve to find the zeroes

x2-1=0

x2-12=0

x+1x-1=0 a2-b2=a+ba-b

x=-1,1

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 =-1+1=0

Again, -ba=-01=0

Product of the zeroes =-11=-1

Again, ca=-11=-1

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

Hence, the zeroes of this polynomial are -1 and 1.


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