Question

What are the solutions to the equation a^2 - 9a + 14 = 0?

a) {-2, 7}
b) {2, -7}
c) {-2, -7}
d) {7, 2}

Answer 1

To find the solutions to the equation a^2 - 9a + 14 = 0, we can use the quadratic formula. The solutions are a = 7 and a = 2.

Step-by-step explanation:

To find the solutions to the equation a^2 - 9a + 14 = 0, we can use the quadratic formula. The quadratic formula states that the solutions to an equation of the form ax^2 + bx + c = 0 are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, the coefficients are a = 1, b = -9, and c = 14. Substituting these values into the quadratic formula, we get:

a = 1, b = -9, c = 14

x = (-(-9) ± √((-9)^2 - 4(1)(14))) / (2(1))

Simplifying the expression further, we get:

x = (9 ± √(81 - 56)) / 2

x = (9 ± √25) / 2

x = (9 ± 5) / 2

This gives us two possible solutions for a:

a = (9 + 5) / 2 = 7

a = (9 - 5) / 2 = 2

Therefore, the solutions to the equation are a = 7 and a = 2. So, the correct answer is option a) {-2, 7}.