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Question

Using quadratic formula solve the following quadratic equation: [3 MARKS]

9x29(a+b)x+(2a2+5ab+2b2)=0

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Solution

Formula: 1 Mark
Steps: 1 Mark
Answer: 1 Mark

We have,

9x29(a+b)x+(2a2+5ab+2b2)=0

Comparing this equation with Ax2+Bx+C=0, we have

A=9,B=9(a+b) and C=2a2+5ab+2b2

D=B24AC

D=81(a+b)236(2a2+5ab+2b2)

D=9a2+9b218ab

D=9(ab)20

D0

So, the roots of the given equation are real and are given by:

α=B+D2A=9(a+b)+3(ab)18=12a+6b18=2a+b3

and, β=BD2A=9(a+b)3(ab)18=6a+12b18=a+2b3

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