Find the values of k for which the given equation has real and equal roots: [3 MARKS]
x2−2x(1+3k)+7(3+2k)=0
Formula: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
The given equation is x2−2x(1+3k)+7(3+2k)=0
Here, a=1,b=−2(1+3k) and c=7(3+2k)
∴D=b2−4ac
⇒D=4(3k+1)2−4×1×7(3+2k)
⇒D=4(9k2+6k+1−21−14k)
⇒D=4(9k2−8k−20)
The given equation will have equal roots, if
D=0
⇒4(9k2−8k−20)=0
⇒9k2−8k−20=0
⇒9k2−18k+10k−20=0
⇒(k−2)(9k+10)=0
⇒k−2=0 or, 9k+10=0⇒k=2 or, k=−109