Question

Y = -2x2 - 12x - 15
What is the x-intercept(s)

Answer 1

`\large \boxed{\left(-3 - \sqrt{(3)/(2)},0\right) \text{ and } \left (-3+ \sqrt{(3)/(2)}, 0\right)}`

Explanation:

Y = -2x² - 12x - 15

Use the quadratic formula:

`x = (-b\pm√(b^2-4ac))/(2a) = (-b\pm√(D))/(2a)`

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

`\begin{array}{rcl}x & = & (-b\pm√(D))/(2a)\\\\ & = & (-(-12)\pm√(24))/(-4)\\\\ & = & (12\pm2√(6))/(-4)\\\\ & = & -3 \pm(√(6))/(2)\\\\ & = & -3 \pm\sqrt{(6)/(4)}\\\\ & = & -3 \pm\sqrt{(3)/(2)}\\\\\end{array}\\\text{The x-intercepts are at $\large \boxed{\mathbf{\left(-3 - \sqrt{(3)/(2)},0\right) \text{ and } \left (-3+ \sqrt{(3)/(2)}, 0\right)}}$}`

The figure below shows the intercepts in decimal form.