Question

determine the value of k so that the quadratic equation 4x^2-2x+k^2-2k+1=0

Answer 1

Answer:

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Answer 2

The value for k is $\frac{1}{2}$, and $\frac{3}{2}$.

Step-by-step explanation:

The given equation is $4x^{2} - 2x + k^{2} -2k+1=0$

$D = b^{2} -4ac$

a = 4

b = -2

c $=k^{2} -2k+1$

$(-2)^{2} -4 (4) (k^{2} -2k+1) = 0$

$4-16(k^{2}-2k+1 )=0$

$4- 16k^{2} +32k-16=0$

$-16k^{2} +32k-16+4=0$

$-16k^{2} +32k-12=0$

$-(16k^{2} -32k+12)=0$

$16k^{2} -32k+12=0$

$4(4k^{2} -8k+3)=0$

$4k^{2}-8k+3=0$

$4k^{2} -6k-2k+3=0$

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

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

$k=\frac{1}{2} , \frac{3}{2}$

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