Find the equation whose roots are \(\frac{3}{4}\) and -4

If a quadratic equation has roots p and q, then it can be expressed in the factored form as:

(x - p)(x - q) = 0

Expanding this equation, we get:

x2 - (p + q)x + pq = 0

In this case, the roots are given as \(\frac{3}{4}\) and -4. Thus, the equation can be expressed as:

(x - \(\frac{3}{4}\))(x + 4) = 0

Expanding this equation, we get:

x2 + (4 - \(\frac{3}{4}\))x - 3 = 0

Multiplying throughout by 4 to eliminate fractions, we get:

4x2 + 13x - 12 = 0

Therefore, the equation whose roots are \(\frac{3}{4}\) and -4 is 4x² + 13x - 12 = 0.

Hence, the answer is 4x² + 13x - 12 = 0.