Question

Use a quadratic equation to find two real numbers whose sum is −13, and whose product is 42. Write the answers from least to greatest.

a) −14,−3
b) −3,−14
c) 14,3
d) 3,14

Answer 1

Using the quadratic formula, the two real numbers are 3 and 14.

Step-by-step explanation:

Using the quadratic formula, we can find the two real numbers that satisfy the given conditions: a sum of -13 and a product of 42.

The quadratic equation is x² - 13x + 42 = 0. Plugging the coefficients into the quadratic formula, we get x = (13 ± √(13² - 4(1)(42))) / 2.

Simplifying further, we find that x = (13 ± √(169 - 168)) / 2, which gives us x = (13 ± √1) / 2.

The solutions are x = (13 + 1) / 2 = 7 and x = (13 - 1) / 2 = 6.

So the answer is d) 3,14.