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Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient.
x22x8

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Solution

Let us first find the zeroes of the given polynomial x22x8 by equating it to 0 as shown below:

x22x8=0x24x+2x8=0x(x4)+2(x4)=0(x+2)(x4)=0(x+2)=0,(x4)=0x=2,x=4

Therefore, the zeroes are 2 and 4.

In the polynomial x22x8, we have a=1,b=2 and 8. Now, consider

Sum of zeroes
2+4=2=(2)1=ba

Product of zeroes
2×4=8=81=ca

Hence, the relation between the zeroes and coefficients is verified.

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