Question

question 9 (mandatory) (1 point) saved
use the quadratic formula to solve $-6x^2 + 5x + 8 = 0$. round your answer to two decimal places.

a) $-0.81$

b) no real solution

c) $-0.81$ and $1.64$

d) $1.64$

Explanation:

Step1: Recall Quadratic Formula

For \(ax^2 + bx + c = 0\), solutions are \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a=-6\), \(b = 5\), \(c = 8\).

Step2: Calculate Discriminant

Discriminant \(D=b^2-4ac=(5)^2-4(-6)(8)=25 + 192 = 217\). Since \(D>0\), two real solutions.

Step3: Compute Solutions

First solution: \(x=\frac{-5+\sqrt{217}}{2(-6)}=\frac{-5 + 14.73}{-12}=\frac{9.73}{-12}\approx - 0.81\).
Second solution: \(x=\frac{-5-\sqrt{217}}{2(-6)}=\frac{-5 - 14.73}{-12}=\frac{-19.73}{-12}\approx1.64\).

Answer:

c) \(-0.81\) and \(1.64\)