1. Find k, for which a root of the quadratic equation is
x^2 +2 (1+3K) x + (3+2K) 7 = 0. is 7.
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Answer: Given x 2 −2x(1+3k)+7(3+2k)=0 has equal roots As we know that For the quadratic equation to have equal roots discriminant should be zero ⟹(−2(1+3k)) 2 −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=− 9 10 ,2 Step-by-step explanation:
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