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

User Gibumba
by
8.8k points

1 Answer

6 votes

Answer:

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

User Haymansfield
by
8.7k points

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