Question

1
select the correct answer.
what are the solutions to this quadratic equation?
$5x^2 - 7x - 18 = 0$
a. $x = \frac{-7 \pm \sqrt{409}}{10}$
b. $x = \frac{7 \pm \sqrt{409}}{5}$
c. $x = \frac{7 \pm \sqrt{409}}{10}$
d. $x = \frac{-7 \pm \sqrt{409}}{5}$

Explanation:

Step1: Identify coefficients

For \(5x^2 -7x -18=0\), \(a=5\), \(b=-7\), \(c=-18\)

Step2: Calculate discriminant

\(\Delta = b^2 -4ac = (-7)^2 -4(5)(-18) = 49 + 360 = 409\)

Step3: Apply quadratic formula

\(x = \frac{-b\pm\sqrt{\Delta}}{2a} = \frac{7\pm\sqrt{409}}{2\times5} = \frac{7\pm\sqrt{409}}{10}\)

Answer:

C. \( x = \frac{7\pm\sqrt{409}}{10} \)