Question

Find the value of k so that the roots of equation x^2+k(4x+k-1)+5=0 has equal roots.
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Answer 1

Secondary SchoolMath 13+7 pts

X2 +k(4x+k-1)+2 find the value of k by which the polynomial hai equal roots

Answers

Answer: k=-1 or 2/3

Step-by-step explanation:

x^2 + k(4x+k-1)+2

= x^2 + 4kx + (k^2-k+2)

When the roots are equal b^2=4ac

So (4k)^2=4*1*(k^2-k+2)

16k^2=4k^2-4k+8

12k^2+4k-8=0

3k^2+k-2=0

(3k-2)(k+1)=0

So k=2/3 or -1

So the polynomial is x^2-4x+4=(x-2)^2

Or

x^2+8x/3+16/9=(x+4/3)^2