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Question

Question 1 (ii)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

4s24s+1

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Solution

4s24s+1

Comparing given polynomial with the general form ax2+bx+c,

We get, a = 4, b = -4 and c = 1.

We have, 4s24s+1 = (2s1)2

The value of 4s24s+1 is zero when (2s1)2 = 0.
s = 12

Therefore, the zeroes of 4s24s+1 are 12 and 12.

Sum of zeroes
= 12+12=1=(4)4=(Coefficient of s)Coefficient of s2

Product of zeroes
=12×12=14=Constant termCoefficient of s2
(Relationship between the zeroes and the coefficients)


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