What are the solutions to the equation x^2-(a-2)x-2a^2+5a-3=0 ?

The solutions to the equation x^2-(a-2)x-2a^2+5a-3=0 are x=2a-3,x=-a+1

Find the zeros of x^2-(a-2)x-2a^2+5a-3=0

The zeros of x^2-(a-2)x-2a^2+5a-3=0 are x=2a-3,x=-a+1

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x^{2} - (a - 2) x - 2 a^{2} + 5 a - 3 = 0

x = 2 a - 3, x = - a + 1

Solution steps

x^{2} - (a - 2) x - 2 a^{2} + 5 a - 3 = 0

Expand

x^{2} - (a - 2) x - 2 a^{2} + 5 a - 3 : x^{2} - a x + 2 x - 2 a^{2} + 5 a - 3

x^{2} - a x + 2 x - 2 a^{2} + 5 a - 3 = 0

Write in the standard form

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

x^{2} + (- a + 2) x - 2 a^{2} + 5 a - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - a + 2 ) \pm ( - a + 2 ) ^{2} - 4 \cdot 1 \cdot ( - 2 a ^{2} + 5 a - 3 )}{2 \cdot 1}

Simplify

(- a + 2)^{2} - 4 \cdot 1 \cdot (- 2 a^{2} + 5 a - 3) : 3 a - 4

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 2 a - 3, x = - a + 1

x^{2} - 6 x - 3 = 0

x^{2} - 2 x - 35

x, x^{2} + x y = 5

x^{2} + 16 x + 68 = 0

x^{2} + 2 x - 10 = 5

What are the solutions to the equation x^2-(a-2)x-2a^2+5a-3=0 ?
The solutions to the equation x^2-(a-2)x-2a^2+5a-3=0 are x=2a-3,x=-a+1
Find the zeros of x^2-(a-2)x-2a^2+5a-3=0
The zeros of x^2-(a-2)x-2a^2+5a-3=0 are x=2a-3,x=-a+1