Question

Determine the number and types of solutions for 6m^2-3m-4=0

Answer 1

Answer:

2 real solutions

Step-by-step explanation:

Remember this messy thing?

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

The quadratic formula, as it's called, gives us the roots to any quadratic equation in standard form (ax² + bx + c = 0). The information on the type of roots is contained entirely in that bit under the square root symbol (b² - 4ac), called the discriminant. If it's non-negative, we'll have real roots, if it's negative, we'll have complex roots.

For our equation, we have a discrimant of (-3)² - 4(6)(-4) = 9 + 96 = 105, which is non-negative, so we'll have real solutions, and since quadratics are degree 2, we'll have exactly 2 real solutions.