Write a quadratic equation with 3/2 and 1/4 as its roots. Write the equation in the form ax2+bx+c=0, where a, b, and c are integers. PLEASE HELP AND SHOW ALL YOUR WORK ILL MARK BRAINLIEST 30 points

Step-by-step explanation:

We have the roots 1/2 and 4/3 and we need to write a quadratic equation of the form a x^{2} +bx+cax

2

+bx+c using those roots. Since we know that 1/2 and 4/3 are roots of our quadratic, we can equate each root to xx and factor backwards:

x= \frac{1}{2}x=

2

1

and x= \frac{4}{3}x=

3

4

2x=12x=1 and 3x=43x=4

2x-1=02x−1=0 and 3x-4=03x−4=0

Now we can multiply the left sides of our equations to get our quadratic:

(2x-1)(3x-4)=6 x^{2} -8x-3x+4=6 x^{2} -11x+4(2x−1)(3x−4)=6x

2

−8x−3x+4=6x

2

−11x+4

W can conclude that the quadratic equation with roots 1/2 and 4/3 is 6x^2-11x+46x

2

−11x+4

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step-by-step explanation: