What are the solutions to the equation roots a^2-x^2+4x-1 ?

The solutions to the equation roots a^2-x^2+4x-1 are x=2-sqrt(a^2+3),x=sqrt(a^2+3)+2

Find the zeros of roots a^2-x^2+4x-1

The zeros of roots a^2-x^2+4x-1 are x=2-sqrt(a^2+3),x=sqrt(a^2+3)+2

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roots

a^{2} - x^{2} + 4 x - 1

x = 2 - a^{2} + 3, x = a^{2} + 3 + 2

Solution steps

a^{2} - x^{2} + 4 x - 1

The roots are the intercepts with the x-axis

(y = 0)

a^{2} - x^{2} + 4 x - 1 = 0

Write in the standard form

a x^{2} + b x + c = 0

- x^{2} + 4 x + a^{2} - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 ( - 1 ) ( a ^{2} - 1 )}{2 ( - 1 )}

Simplify

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

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

Separate the solutions

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

x = \frac{- 4 + 2 a ^{2} + 3}{2 ( - 1 )} : 2 - a^{2} + 3

x = \frac{- 4 - 2 a ^{2} + 3}{2 ( - 1 )} : a^{2} + 3 + 2

The solutions to the quadratic equation are:

x = 2 - a^{2} + 3, x = a^{2} + 3 + 2

1 = 3 x^{2} - 2

x (x + 8) - 4 (5 x + 7) = 0

x, 4 x^{2} - 3 y^{2} + 12 z^{2} + 12 = 0

0 = - 4 x^{2} - 16 x - 12

n^{2} + 7 n + 15 = 5

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