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21.07.2022 - 10:28

Find the roots, x_1 and x_2, of x2 – 5x -14 = 0.

Question:

Find the roots, {eq}x_1 {/eq} and {eq}x_2 {/eq}, of {eq}x^2 – 5x -14 = 0{/eq}.

Answers (1)

June April 18, 2023 в 14:11

To find the roots of a \quadratic equation {eq}ax^2 + bx + c = 0{/eq}, we can use the \quadratic formula: {eq}x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} {/eq} In this case, we have {eq}a = 1{/eq}, {eq}b = -5{/eq}, and {eq}c = -14{/eq}. Substituting these values into the formula, we get: {eq}x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-14)}}{2(1)} {/eq} Simplifying: {eq}x = \frac{5 \pm \sqrt{25 + 56}}{2} {/eq} {eq}x = \frac{5 \pm \sqrt{81}}{2} {/eq} {eq}x = \frac{5 pm 9}{2} {/eq} So, the roots are {eq}x_1 = -2{/eq} and {eq}x_2 = 7{/eq}. We can check that these are indeed the roots by substituting them back into the original equation and verifying that it holds true.

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