Question
If the equation x2+2(k+2)x+9=0 has equal roots, then find the values of k.
Answer: Option C
:
C
Step 1:- x2+2(k+2)x+9=0, ⇒a=1,b=2(k+2),c=9
D=4(k+2)2–4(9)=4(k2+4k−5) [D=b2−4ac ]
Step 2:- The roots of quadratic equation are real and equal only when D=0
4(k2+4k−5)=0,⇒k2+4k−5=0
Step 3:- k2+4k−5=0
⇒k2+5k−k−5=0
⇒k(k+5)−1(k+5)=0
⇒(k−1)(k+5)=0
⇒k=1ork=−5
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:
C
Step 1:- x2+2(k+2)x+9=0, ⇒a=1,b=2(k+2),c=9
D=4(k+2)2–4(9)=4(k2+4k−5) [D=b2−4ac ]
Step 2:- The roots of quadratic equation are real and equal only when D=0
4(k2+4k−5)=0,⇒k2+4k−5=0
Step 3:- k2+4k−5=0
⇒k2+5k−k−5=0
⇒k(k+5)−1(k+5)=0
⇒(k−1)(k+5)=0
⇒k=1ork=−5
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