Question

How do you use the quadratic formula to find both solutions to the quadratic equation `x^2-5x-14=0`?

Answer 1

Solve `y = x^2 - 5x - 14 = 0.`

Explanation:

`D = d^2 = b^2 - 4ac = 25 + 56 = 81 -->`d = +- 9#

`x = -b/(2a) +- d/(2a) = 5/2 +- 9/2` --> x = 7 and x = -2

There is another method that may be faster. Roots have opposite signs (Rule of signs)
Factor pairs of (-14) -> (-1, 14)(-2, 7). This sum is 5 = -b. Then, the 2 real roots are: -2 and 7.