Question

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

Answer 1

16x² + 8x - 15 = 0

Explanation:

Given the roots are x = -
`(5)/(4)` and x =
`(3)/(4)`, then the factors are

(x +
`(5)/(4)` ) and (x -
`(3)/(4)` ) and the equation is

(x +
`(5)/(4)` )(x -
`(3)/(4)` ) = 0 ← expand factors using FOIL

x² -
`(3)/(4)` x +
`(5)/(4)` x -
`(15)/(16)` = 0, that is

x² +
`(1)/(2)` x -
`(15)/(16)` = 0 ( multiply through by 16 )

16x² + 8x - 15 = 0