What are the solutions to the equation x^2+2kx+(k-1)(k-3)=0 ?

The solutions to the equation x^2+2kx+(k-1)(k-3)=0 are x=-k+sqrt(4k-3),x=-k-sqrt(4k-3)

Find the zeros of x^2+2kx+(k-1)(k-3)=0

The zeros of x^2+2kx+(k-1)(k-3)=0 are x=-k+sqrt(4k-3),x=-k-sqrt(4k-3)

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x^{2} + 2 k x + (k - 1) (k - 3) = 0

x = - k + 4 k - 3, x = - k - 4 k - 3

Solution steps

x^{2} + 2 k x + (k - 1) (k - 3) = 0

Expand

x^{2} + 2 k x + (k - 1) (k - 3) : x^{2} + 2 k x + k^{2} - 4 k + 3

x^{2} + 2 k x + k^{2} - 4 k + 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 k \pm ( 2 k ) ^{2} - 4 \cdot 1 \cdot ( k ^{2} - 4 k + 3 )}{2 \cdot 1}

Simplify

(2 k)^{2} - 4 \cdot 1 \cdot (k^{2} - 4 k + 3) : 2 - 3 + 4 k

x_{1, 2} = \frac{- 2 k \pm 2 - 3 + 4 k}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 2 k + 2 - 3 + 4 k}{2 \cdot 1}, x_{2} = \frac{- 2 k - 2 - 3 + 4 k}{2 \cdot 1}

x = \frac{- 2 k + 2 - 3 + 4 k}{2 \cdot 1} : - k + 4 k - 3

x = \frac{- 2 k - 2 - 3 + 4 k}{2 \cdot 1} : - k - 4 k - 3

The solutions to the quadratic equation are:

x = - k + 4 k - 3, x = - k - 4 k - 3

4 x^{2} - 25 x + 36 = 0

2 x^{2} - 4 x + 13 = 9

4 x (1 + x) = 0

x^{2} - 10.24 x + 2.56 = 0

x^{2} + 10 x + 25 = 0

What are the solutions to the equation x^2+2kx+(k-1)(k-3)=0 ?
The solutions to the equation x^2+2kx+(k-1)(k-3)=0 are x=-k+sqrt(4k-3),x=-k-sqrt(4k-3)
Find the zeros of x^2+2kx+(k-1)(k-3)=0
The zeros of x^2+2kx+(k-1)(k-3)=0 are x=-k+sqrt(4k-3),x=-k-sqrt(4k-3)