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------------------------------------------------ Write a quadratic equation in standard form with integral coefficients, given the roots -8.3 and 1. Begin your equation with "y =" and use "x" as the independent variable. Note: the coefficients used in your equation should not have any common factors.

Hint: It's not [tex]y = x^2 + 7.3x - 8.3[/tex].

To write the quadratic equation, we can use the sum and product of roots formulas. By setting up equations based on the given roots and solving for the coefficients, we can find the quadratic equation in standard form with integral coefficients.

Explanation:

To write a quadratic equation in standard form with integral coefficients given the roots -8.3 and 1, we can use the fact that the sum and product of the roots of a quadratic equation can be determined using the following formulas:

Sum of roots: (-b/a)

Product of roots: (c/a)

Let's assume that the equation is y = ax^2 + bx + c. From the given roots, we have the following equations:

-8.3 + 1 = (-b/a)

(-8.3)(1) = (c/a)

Simplifying these equations, we get:

-7.3 = (-b/a)

-8.3a = c

To avoid common factors, we can select a = 10 and b = 73. Substituting these values into the equation y = ax^2 + bx + c, we have:

y = 10x^2 + 73x - 83

So, the quadratic equation in standard form with integral coefficients and given roots -8.3 and 1 is y = 10x^2 + 73x - 83.

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