Question

Find the quadratic equation whose roots are -5/4 and 3/4

Answer 1

Answer:

16x² + 8x - 15 = 0

Step-by-step explanation:

Given the roots are x = - $\frac{5}{4}$ and x = $\frac{3}{4}$, then the factors are

(x + $\frac{5}{4}$ ) and (x - $\frac{3}{4}$ ) and the equation is

(x + $\frac{5}{4}$ )(x - $\frac{3}{4}$ ) = 0 ← expand factors using FOIL

x² - $\frac{3}{4}$ x + $\frac{5}{4}$ x - $\frac{15}{16}$ = 0, that is

x² + $\frac{1}{2}$ x - $\frac{15}{16}$ = 0 ( multiply through by 16 )

16x² + 8x - 15 = 0