Question

question
what are the roots of the equation $4x^2 - 24x + 37 = 0$ in simplest $a + bi$ form?
answer
attempt 1 out of 2
+ additional solution - no solution
$x = \square$ submit answer
$\sqrt{}$ $\pm$

Explanation:

Step1: Identify coefficients for quadratic formula

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 4\), \(b = -24\), \(c = 37\).

Step2: Calculate discriminant \(\Delta = b^2 - 4ac\)

\(\Delta = (-24)^2 - 4\times4\times37 = 576 - 592 = -16\)

Step3: Apply quadratic formula \(x=\frac{-b\pm\sqrt{\Delta}}{2a}\)

\(x=\frac{-(-24)\pm\sqrt{-16}}{2\times4}=\frac{24\pm4i}{8}\)

Step4: Simplify the fraction

Divide numerator terms by 8: \(x = 3\pm\frac{1}{2}i\)

Answer:

\(3 \pm \frac{1}{2}i\)