K 4 x 2 k 1 x 1 0
Asked by admin @ in Math viewed by 399 People
Solve : (k+4)x2+(k+1)x +1=0 has equal roots . find the value of k.also find the roots
Answered by admin @
Hi friend!!
We know that, for a given equation ax²+bx+c=0 to have equal roots, the required condition is
b²-4ac=0
Given,
(k+4)x²+(k+1)x +1=0 has equal roots
→(k+1)²-4(k+4)=0
k²+1+2k-4k-16=0
k²-2k-15=0
k²-5k+3k-15=0
k(k-5)+3(k-5)=0
(k+3)(k-5)=0
k=-3,5
If k=-3
Now, the polynomial becomes
(k+4)x²+(k+1)x +1=0
(-3+4)x²+(-3+1)x+1=0
x²-2x+1=0
(x-1)²=0
x=1
If k=5
Now, the polynomial becomes
(k+4)x²+(k+1)x +1=0
9x²+6x+1=0
9x²+3x+3x+1=0
3x(3x+1)+1(3x+1)=0
(3x+1)²=0
3x+1=0
x=-1/3
Now, the roots are 1 (or)-1/3
I hope this will help you;)
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