Question
If the equation x2+2(k+2)x+9k=0 has equal roots, then values of k are __________.
Answer: Option A
:
A
Step 1:- For, x2+2(k+2)x+9k=0, value of discriminant D=[2(k+2)]2–4(9k)=4(k2+4−5k)
Step 2:- The roots of quadratic equation are real and equal only when D=0
k2+4−5k=0
⇒k2−5k+4=0
⇒k2−k−4k+4=0
⇒k(k−1)−4(k−1)=0
⇒(k−1)(k−4)=0
Step 3:- k=4or1
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:
A
Step 1:- For, x2+2(k+2)x+9k=0, value of discriminant D=[2(k+2)]2–4(9k)=4(k2+4−5k)
Step 2:- The roots of quadratic equation are real and equal only when D=0
k2+4−5k=0
⇒k2−5k+4=0
⇒k2−k−4k+4=0
⇒k(k−1)−4(k−1)=0
⇒(k−1)(k−4)=0
Step 3:- k=4or1
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