Which of the following quadratic equation has 2/3 and -1/4 as their roots. Created by margauxz. Math

4 as their roots...

September 2022 2 10 Report

Which of the following quadratic equation has 2/3 and -1/4 as their roots

Answer:

Step-by-step explanation:

Given (roots):

x = ²/₃

x = -¹/₄

$x = \frac{2}{3}\\3\times x=\frac{2}{3}\times 3\\3x = 2\\3x - 2=2 - 2\\3x - 2 =0$

$x = -\frac{1}{4}\\4\times x = -\frac{1}{4}\times4\\4x=-1\\4x+1=-1+1\\4x+1=0$

The two factors are (3x - 2) and (4x + 1).

Use the FOIL method:

(3x - 2)(4x + 1)

= (3x)(4x) + (3x)(1) + (-2)(4x) + (-2)(1)

= 12x² + 3x - 8x - 2

= 12x² - 5x - 2

#CarryOnLearning

Answer and Explanation:

The roots of a quadratic equation are 2/3 and -1/4.

It is can be written as (x - 2/3)(x + 1/4) when finding its quadratic equation.

Multiply (x - 2/3)(x + 1/4).

The answer will be:

${x}^{2} - \frac{5}{12}x - \frac{1}{6}$