use the discriminate to determain the number of real solutions to each solution

Question

7x^2-8x-8=2

Answer 1

To determine the number of real solutions, we can use the discriminant, which is given by the formula B^2 - 4AC, where the quadratic equation is in the form Ax^2 + Bx + C = 0.

In this case, the equation is 7x^2 - 8x - 8 = 2. We can rewrite this equation as 7x^2 - 8x - 10 = 0.

Comparing this equation with the general quadratic equation form Ax^2 + Bx + C = 0, we have:
A = 7, B = -8, and C = -10.

Now, let's calculate the discriminant:
Discriminant = B^2 - 4AC = (-8)^2 - 4(7)(-10) = 64 + 280 = 344.

Since the discriminant is positive (344 > 0), the quadratic equation has two distinct real solutions.