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Kamila [148]
3 years ago
6

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

Mathematics
1 answer:
drek231 [11]3 years ago
4 0

Answer:

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

Step-by-step explanation:

<u>Nature of Roots of a Second-Degree Equation</u>

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.

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