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Question

Find the values of k for which the given equation has real and equal roots: [3 MARKS]

x22x(1+3k)+7(3+2k)=0

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Solution

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

The given equation is x22x(1+3k)+7(3+2k)=0

Here, a=1,b=2(1+3k) and c=7(3+2k)

D=b24ac

D=4(3k+1)24×1×7(3+2k)

D=4(9k2+6k+12114k)

D=4(9k28k20)

The given equation will have equal roots, if

D=0

4(9k28k20)=0

9k28k20=0

9k218k+10k20=0

(k2)(9k+10)=0

k2=0 or, 9k+10=0k=2 or, k=109


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