MAC1106 Advanced Algebra EXAM w/ RATIONALES 2026 Complete And Study material 14pages LEARNEXAMS

What is the solution set to the equation 4x^2 + 9x - 7 = 0?

a) {x = -1, x = 7/4}

b) {x = 1/4, x = -7/4}

c) {x = -7/4, x = 1/4}

d) {x = 7/4, x = -1}

Answer: c) {x = -7/4, x = 1/4}

Rationale: This is a quadratic equation. To find the solution

set, we can use the quadratic formula. Plugging in the

coefficients, we have x = (-9 ± √(9^2 - 4(4)(-7))) / (2(4)).

Simplifying the expression gives us x = (-9 ± √(81 + 112)) /

8, which further simplifies to x = (-9 ± √(193)) / 8.

Therefore, the solution set is {x = -7/4, x = 1/4}.

2.

Solve the inequality 2x^2 - 5x > 3.

a) x < -1/2 or x > 3

b) x < -3 or x > 1/2

c) x < -1/2 or x > 1/2

d) x < -3 or x > 2

Answer: a) x < -1/2 or x > 3

Rationale: To solve the inequality, we first set it equal to