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

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

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

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

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

x = m - 2, x = - 3 m

Solution steps

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

Expand

x^{2} + 2 (m + 1) x - 3 m (m - 2) : x^{2} + 2 m x + 2 x - 3 m^{2} + 6 m

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

Write in the standard form

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

x^{2} + (2 m + 2) x - 3 m^{2} + 6 m = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( 2 m + 2 ) \pm ( 2 m + 2 ) ^{2} - 4 \cdot 1 \cdot ( - 3 m ^{2} + 6 m )}{2 \cdot 1}

Simplify

(2 m + 2)^{2} - 4 \cdot 1 \cdot (- 3 m^{2} + 6 m) : 2 (2 m - 1)

x_{1, 2} = \frac{- ( 2 m + 2 ) \pm 2 ( 2 m - 1 )}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( 2 m + 2 ) + 2 ( 2 m - 1 )}{2 \cdot 1}, x_{2} = \frac{- ( 2 m + 2 ) - 2 ( 2 m - 1 )}{2 \cdot 1}

x = \frac{- ( 2 m + 2 ) + 2 ( 2 m - 1 )}{2 \cdot 1} : m - 2

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

The solutions to the quadratic equation are:

x = m - 2, x = - 3 m

x, f = f (x^{2}) - 2 f (1)

x, x^{2} + y^{2} + z^{2} - 25 = 0

- x^{2} + 10 x + 24 = 0

x, g = 2 x^{2} + x - 3 g (- 2)

x^{2} - 1 = x - 2

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