Question

Find the x-intercepts of the graph of the equation. $$y=3 x^{2}+20 x+1$$

Short answer

The x-intercepts of the graph of the equation are -0.05 and -6.62.

Step-by-step solution

Identify a, b, and c

The general form of a quadratic equation is \(ax^{2}+bx+c\). In this equation, a=3, b=20, and c=1.

Substitute a, b, and c to the quadratic formula

Substitute a=3, b=20, and c=1 into the quadratic formula to get \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{-20\pm\sqrt{(20)^{2}-4*3*1}}{2*3}\).

Simplify the equation

Simplify the equation to get \(x=\frac{-20\pm\sqrt{400-12}}{6}=\frac{-20\pm\sqrt{388}}{6}\).

Find two values of x

Obtain the two values of x by solving \(x=\frac{-20+\sqrt{388}}{6}\) and \(x=\frac{-20-\sqrt{388}}{6}\). After calculation, the approximate values of x are -0.05 and -6.62.