QuadraticThe quadratic equation has roots x=2/3 and x=-4. Find one set of possible values for a,b,c.

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The form of the quadratic is ax^2 + bx + c = 0

We'll write the quadratic as a product of linear factors:

ax^2 + bx + c = (x - 2/3)(x+4)

ax^2 + bx + c = x^2 + 4x - 2x/3 - 8/3

Comparing both sides, we'll get:

a = 1

b = 4 - 2/3

b = 10/3

c = -8/3

Applying Viete's relations, yields

x1 + x2 = -b/a

But, from enunciation, x1 = 2/3 and x2 = -4:

2/3 - 4 = -b/a

We'll multiply by 3:

-10/3 = -b/a

b/a = 10/3

10a = 3b

x1*x2 = c/a

-8/3 = c/a

-8a = 3c

The requested quadratic equation is: 3x^2 + 10x - 8 = 0

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