Answer:
[tex]\large \boxed{\left(-3 - \sqrt{\frac{3}{2}},0\right) \text{ and } \left (-3+ \sqrt{\frac{3}{2}}, 0\right)}[/tex]
Step-by-step explanation:
Y = -2x² - 12x - 15
Use the quadratic formula:
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]
a = -2; b = -12; c = -15
1. Evaluate the discriminant D
D = b² - 4ac = (-12)² - 4(-2)(-15) = 144 - 120 = 24
2. Solve for x
[tex]\begin{array}{rcl}x & = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-(-12)\pm\sqrt{24}}{-4}\\\\ & = & \dfrac{12\pm2\sqrt{6}}{-4}\\\\ & = & -3 \pm\dfrac{\sqrt{6}}{2}\\\\ & = & -3 \pm\sqrt{\dfrac{6}{4}}\\\\ & = & -3 \pm\sqrt{\dfrac{3}{2}}\\\\\end{array}\\\text{The x-intercepts are at $\large \boxed{\mathbf{\left(-3 - \sqrt{\frac{3}{2}},0\right) \text{ and } \left (-3+ \sqrt{\frac{3}{2}}, 0\right)}}$}[/tex]
The figure below shows the intercepts in decimal form.
