Question

Find the value of k for which the equation 2x + k (2x + k – 1) + 4 =

0 has real and equal roots​

Answer 1

Answer:

Solution:

As the question says, the roots of the equation are equal. Let us take the roots as\alphaα , \betaβ

Now we can say that \alpha=\beta=mα=β=m

Therefore, the equation is x^{2}+k 2 x+k^{2}-k+2x

2

+k2x+k

2

−k+2 which means if put according to a x^{2}+b x+cx

2

+bx+c ,

Then the sum of root is, \alpha+\beta=-\frac{b}{a}bα+β=−

a

b

b

that is2 m=-\frac{2 k}{1}2m=−

1

2k

and

\alpha \beta=\frac{c}{a}=\frac{k^{2}-k+2}{1}.αβ=

a

c

=

1

k

2

−k+2

.

Therefore,

\boldsymbol{m}=\boldsymbol{k} \& \boldsymbol{m}^{2}=\boldsymbol{k}^{2}-\boldsymbol{k}+\mathbf{2}m=k&m

2

=k

2

−k+2

Put the value of m = k inm^{2}=k^{2}-k+2m

2

=k

2

−k+2 we get

k^{2}=k^{2}-k+2k

2

=k

2

−k+2

k=2

Therefore, the value of k = 2.

Step-by-step explanation:

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