Question

The table shows input and output values of the function y = x2 + 12x – 2. What is an approximate solution of the equation x2 + 12x – 2 = 0?

Answer 1

Answer:

The solutions for the equations are x = 0.1644 and x = -12.1644

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$.

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$, given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$x^{2} + 12x - 2 = 0$

So

$a = 1, b = 12, c = -2$

$\bigtriangleup = 12^{2} - 4*1*(-2) = 152$

$x_{1} = \frac{-12 + \sqrt{152}}{2} = 0.1644$

$x_{2} = \frac{-12 - \sqrt{152}}{2} = -12.1644$

The solutions for the equations are x = 0.1644 and x = -12.1644