Question

Write an equation that defines m(x) as a trinomial where m(x) = (3x - 1)(3 - x) + 4x^2 + 19.

Solve for x when m(x) = 0.

Answer 1

m(x) = (3x - 1)(3 - x) + 4x² + 19
0 = 3x(3 - x) - 1(3 - x) + 4x² + 19
0 = 3x(3) - 3x(x) - 1(3) + 1(x) + 4x² + 19
0 = 9x - 3x² - 3 + x + 4x² + 19
0 = -3x² + 4x² + 9x + x - 3 + 19
0 = x² + 10x + 16
x = -(10) ± √((10)² - 4(1)(16))
2(1)
x = -10 ± √(100 - 64)
2
x = -10 ± √(36)
2
x = -10 ± 6
2
x = -5 ± 3
x = -5 + 3 U x = -5 - 3
x = -2 U x = -8

Answer 2

m(x) = (3x - 1)(3 - x) + 4x^2 + 19
0 = 9x - 3x^2 - 3 + x + 4x^2 + 19
0 = x^2 + 10x + 16
now use quadratic formula
a = 1 b = 10 c = 16
x = -b +/- √b²-4ac ÷ 2a
x = -10 +/- √100 - 4(16) ÷ 2
x = -10 +/- √100-64 ÷ 2
x = -10 +/- √36 ÷ 2
split the equation
x = -10 - 6 ÷ 2 and x = -10 + 6 ÷ 2
x = -16 ÷ 2 x = -4 ÷ 2
x = -8 x = -2
so the value for x are -8 and -2