Question

question 1 of 5

select the correct answer.

what are the solutions of this quadratic equation?

\\4x^2 - 40x + 109 = 0\\

\\(x = -5 \pm \frac{3}{2}i\\)

\\(x = 5 \pm \frac{3}{2}i\\)

\\(x = -5 \pm 12i\\)

\\(x = 5 \pm 12i\\)

Explanation:

Identify the coefficients of the quadratic equation

$$ a = 4, \quad b = -40, \quad c = 109 $$

Apply the quadratic formula

$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

$$ x = \frac{-(-40) \pm \sqrt{(-40)^2 - 4(4)(109)}}{2(4)} $$

Simplify the expression

$$ x = \frac{40 \pm \sqrt{1600 - 1744}}{8} $$

$$ x = \frac{40 \pm \sqrt{-144}}{8} $$

$$ x = \frac{40 \pm 12i}{8} $$

$$ x = 5 \pm \frac{3}{2}i $$

Answer:

• \(x = -5 \pm \frac{3}{2}i\)
• \(x = 5 \pm \frac{3}{2}i\) (Correct answer)
• \(x = -5 \pm 12i\)
• \(x = 5 \pm 12i\)