Answer:
12x^2 + 9x - 8 = 0
Explanation:
To find the quadratic equation with roots 2/3 and -3/4, we can use the fact that if a quadratic equation has roots r and s, then it can be written in the form:
(x - r)(x - s) = 0
Expanding this equation gives:
x^2 - (r + s)x + rs = 0
So, for the roots 2/3 and -3/4, we have:
(x - 2/3)(x + 3/4) = 0
Expanding this equation gives:
x^2 + (3/4 - 2/3)x - (2/3)(3/4) = 0
Multiplying through by 12 to eliminate the fractions, we get:
12x^2 + 9x - 8 = 0
So, the quadratic equation with roots 2/3 and -3/4 is:
12x^2 + 9x - 8 = 0