Find the value of k for equal roots in quadratic equation x2-2x(1+3k)-7(3+2k)=0
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Step-by-step explanation: Given x2 −2x(1+3k)+7(3+2k)=0 has equal roots
we know that
For the quadratic equation to have equal roots discriminant should be zero
⟹(−2(1+3k)) 02
−4(1)(7(3+2k))=0
⟹4(1+3k) 2 −28(3+2k)=0
⟹(9k 2 +6k+1)−21−14k=0
⟹9k 2 −8k−20=0
⟹9k 2 −18k+10k−20=0
⟹9k(k−2)+10(k−2)=0
⟹(9k+10)(k−2)=0
⟹k=− 10/9 ,2
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