How many solutions does 5 h^(2)=14 have?

Answer 1

The equation 5h^2 = 14 is a quadratic equation. A quadratic equation can have 0, 1, or 2 solutions depending on the discriminant (the part inside the square root in the quadratic formula).

In this case, the equation can be rewritten as h^2 = 14/5 or h^2 - 14/5 = 0.

The discriminant for a quadratic equation in the form ax^2 + bx + c = 0 is given by b^2 - 4ac.

For this equation, a = 1, b = 0, and c = -14/5. The discriminant is:

0 - 4(1)(-14/5) = 56/5

Since the discriminant is positive, the equation has 2 real solutions.