How do you find the roots, real and imaginary, of y= (2x+1)^2-(x + 1) (x - 4) using the quadratic formula?

1 Answer
Roella W.
Jan 6, 2016

x =( -5+sqrt(5))/10 or x=(-5-sqrt(5))/10

Explanation:

First expand the equation to get it into standard form.
y = (2x+1)^2 - (x+1)(x-4)
y = (4x^2 +2x +1) - (x^2 -3x -4)
y = 3x^2 +5x +5
Now use the quadratic formula x = (-b +-sqrt(b^2 - 4ac))/(2a) to find the values of x for which y=0
x = (-5 +-sqrt(5^2 -4*1*5))/(2*1*5)
x = (-5 +- sqrt(5))/10
x =( -5+sqrt(5))/10 or x=(-5-sqrt(5))/10

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