Which of the following is equivalent to x2 - 13x + 40?

Question

ScanSolve AI Tutor · Accepted Answer

Let's find the roots of the equation.

The equation given is $2x^2 - 13x + 15 = 0$ .

Identify the coefficients of the quadratic equation.
For a quadratic equation in the form $ax^2 + bx + c = 0$ , we have:
$a = 2$
$b = -13$
$c = 15$
Use the quadratic formula to find the roots.
The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Substitute the values of a, b, and c into the formula:
$x = \frac{-(-13) \pm \sqrt{(-13)^2 - 4(2)(15)}}{2(2)}$ $x = \frac{13 \pm \sqrt{169 - 120}}{4}$ $x = \frac{13 \pm \sqrt{49}}{4}$ $x = \frac{13 \pm 7}{4}$
Calculate the two possible roots.
For the positive case:
$x_1 = \frac{13 + 7}{4} = \frac{20}{4} = 5$
For the negative case:
$x_2 = \frac{13 - 7}{4} = \frac{6}{4} = \frac{3}{2}$
The roots of the equation are 5 and $\frac{3}{2}$ .
Compare the calculated roots with the given options.
The options are:
A. $\frac{5}{2}$
B. $\frac{3}{2}$
C. 5
D. 3

Both $\frac{3}{2}$ (Option B) and 5 (Option C) are roots of the equation. Since this is a multiple-choice question and both are correct, we will select one of them.

The correct option is B.

The roots of the equation are $\boxed{\text{B. } \frac{3}{2} \text{ (and also C. } 5)}$ .

Answer