Question

What are the exact solutions of x^2 − 3x − 7 = 0?

Answer 1

Given:

The given equation is $x^{2} -3x-7=0$

We need to determine the exact solutions of the equation.

Exact solution:

The exact solution of the equation can be determined by solving the equation using quadratic formula,

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

From the equation the values are a = 1, b = -3 and c = -7

Thus, substituting these values in the equation, we get;

$x=\frac{-(-3) \pm \sqrt{3^2-4(1)(-7)}}{2(1)}$

$x=\frac{3 \pm \sqrt{9+28}}{2}$

$x=\frac{3 \pm \sqrt{37}}{2}$

Thus, the exact solutions of the given equation is $x=\frac{3 \pm \sqrt{37}}{2}$

Hence, Option A is the correct answer.