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Find the equation whose roots are \(\frac{2}{3}and \frac{-1}...

Find the equation whose roots are $\frac{2}{3}and \frac{-1}{4}$

A.

$12x^2-5x+2=0$

B.

$12x^2-11x+2=0$

C.

$x^2-\frac{11}{12}x+2=0$

D.

$x^2+\frac{11}{12}x-2=0$

E.

$12x^2+11x+2=0$

View answer & explanation

Correct answer is A

x $^2$ - (sum of given roots)x + (product of given roots ) = 0
x $^2$ - ( $\frac{2}{3} + \frac{-1}{4}$ )x + ( $\frac{2}{3} * \frac{-1}{4}$ ) = 0

x $^2$ - ( $\frac{8 - 3}{12}$ )x + ( $\frac{- 2}{12}$ )

x $^2$ - $\frac{5}{12}$ x + $\frac{- 2}{12}$

multiply through by the LCM 12

12 * x $^2$ - 12 * $\frac{5}{12}$ x + 12 * $\frac{- 2}{12}$

12x $^2$ - 5x - 2 = 0

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