The solutions to the given quadratic equation [2x² - 3x - 4 = 0] are x = 2.35, -8.85.
The solutions to the given quadratic equation [x² + 2x + 2 = 0] are x = -1+i, -1-i.
What are the solutions to the quadratic equation?
Given the equation for the general quadratic formular;
[ -b±√( b² - 4(ac)) ]/2a
a) 2x² - 3x - 4 = 0
We substitute into the equation.
x = [ -(-3)±√(-3)² - 4( 2 × -4 )) ] / 2×2
x = [ 3±√9 + 32 ] / 4
x = [ 3±√41 ] / 4
x = [ 3+√41 ] / 4, [ 3-√41 ] / 4
x = 2.35, -8.85
The solutions to the given quadratic equation [2x² - 3x - 4 = 0] are x = 2.35, -8.85
b) x² + 2x + 2 = 0
We substitute into the equation.
x = [ -2±√( 2² - 4( 1×2 )) ] / 2×1
x = [ -2±√( 4 - 8) ] / 2
x = [ -2±√(-4) ] / 2
Lets re-write -4 as -1( 4 )
x = [ -2±√( -1 × 4) ] / 2
x = [ -2±√4 × √-1 ] / 2
Write √-1 as i
x = [ -2±√4 × i] / 2
x = [ -2± 2 × i] / 2
x = 2[ -1 ± i] / 2
x = (-1 ± i)
x = -1+i, -1-i
The solutions to the given quadratic equation [x² + 2x + 2 = 0] are x = -1+i, -1-i.
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