Question

1. What is the sum of the two solutions to the equation 3x2 - x = 4?

Answer 1

Answer:

The sum of the two solutions to the given equation is 1/3.

Step-by-step explanation:

Nature of Roots of a Second-Degree Equation

Given a quadratic equation:

$ax^2 + bx + c = 0$

The roots of the equation are:

$\displaystyle x_1=\frac{-b+ \sqrt{b^2-4ac}}{2a}$

$\displaystyle x_2=\frac{-b- \sqrt{b^2-4ac}}{2a}$

The sum of the roots is:

$\displaystyle x_1+x_2=-\frac{b}{a}$

The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient.

We are given the equation:

$3x^2 - x = 4$

Rearranging:

$3x^2 - x - 4=0$

The coefficient b is b=-1, and the leading coefficient is a=3, thus the sum of the roots is:

$\displaystyle x_1+x_2=-\frac{-1}{3}$

$\displaystyle x_1+x_2=\frac{1}{3}$

The sum of the two solutions to the given equation is 1/3.