Which one of the following interval(s) is the set solution of the quadratic inequality 10x2 – 4x – 6 < 8x2 + 4x – 12?a.(-∞,1) U (3, ∞)b.(-∞,1)c.(1, 3)d.(3, ∞)

To solve the quadratic inequality 10x^2 – 4x – 6 < 8x^2 + 4x – 12, we first need to bring all terms to one side of the inequality.

Subtract 8x^2, add 4x and add 12 to both sides to get:

2x^2 - 8x + 6 < 0

Next, we factor the quadratic expression:

2(x - 1)(x - 3) < 0

Setting each factor equal to zero gives the critical points x = 1 and x = 3.

We then test the intervals determined by these critical points in the inequality.

For x < 1, both factors are negative, so the product is positive.

For 1 < x < 3, the factor (x - 1) is positive and the factor (x - 3) is negative, so the product is negative.

For x > 3, both factors are positive, so the product is positive.

Therefore, the solution to the inequality is the interval where the product is less than zero, which is (1, 3).

So, the correct answer is c. (1, 3).