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.