Answer:
16x² + 8x - 15 = 0
Step-by-step explanation:
Given the roots are x = - [tex]\frac{5}{4}[/tex] and x = [tex]\frac{3}{4}[/tex], then the factors are
(x + [tex]\frac{5}{4}[/tex] ) and (x - [tex]\frac{3}{4}[/tex] ) and the equation is
(x + [tex]\frac{5}{4}[/tex] )(x - [tex]\frac{3}{4}[/tex] ) = 0 ← expand factors using FOIL
x² - [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{4}[/tex] x - [tex]\frac{15}{16}[/tex] = 0, that is
x² + [tex]\frac{1}{2}[/tex] x - [tex]\frac{15}{16}[/tex] = 0 ( multiply through by 16 )
16x² + 8x - 15 = 0
