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faust18 [17]
3 years ago
13

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

Mathematics
1 answer:
meriva3 years ago
5 0

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

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