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In $3-14$ , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. $$2 x^{2}=x+4$$

$\frac{1+\sqrt{33}}{4}$ and $\frac{1-\sqrt{33}}{4}$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 2

The Quadratic Formula

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

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Lectures

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In mathematics, the absolu…

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In $3-14$ , use the quadra…

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in this exercise, we want to use the quadratic formula to find our roots. So first wait to get into the form of a X squared plus bx C to use our formula. So if we subtract execrable sides to track for, both sides will get theirs. We have two X squared minus X minus four equals zero and now they can use our quadratic formula. And that would be opposite Be a plus or minus squared of B squared minus for a C over to a Let's begin. So negative b is going to be negative. Negative one. So we have one plus or minus the square root of B squared, which is going to be negative. One squared one minus four times A, which is two times C, which is negative for over two. A where a. Here's two, so two times two is four. Let's simplify with Insider Square. Here you have one minus four times two times before, which is the same as one plus four times, two times four. So four times he has 88 times four is 32. This equals 33 so we can rewrite this as one plus or minus the square root of 33 over four. So we can't actually simplify this square anymore. Because 33 is just three times 11. Those are both prime, so there's there's no way to score there. You can rewrite our roots as one plus the square root of 33 over four and one minus squared of 33 over four. Those are our roots.

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