Write the quadratic equation in standard form with roots of -1/4 and 2/3 through (2,10) (no fractions in final answer)

Question

Jeffrey Jordon · Accepted Answer

A quadratic equation is an equation of the form:

$x^{2} + p * x + q = 0$ ,

where p is the coefficient of x, q is the free term.

According to Vieta's theorem, the sum of the roots of the quadratic equation is equal to the coefficient of x with the opposite sign, that is:
$x_{1} + x_{2} = - p .$

Also, according to Vieta's theorem, the roots of the quadratic equation is equal to the free term, that is:

$x_{1} * x_{2} = q .$

Given $x_{1} = - \frac{1}{4}$ and $x_{2} = \frac{2}{3}$ .

Thus:

1) $- \frac{1}{4} + \frac{2}{3} = p$
Multiply the first fraction by 3, the second by 4 (general denominator)
$= - \frac{3}{12} + \frac{8}{12} = \frac{- 3 + 8}{12} = - \frac{5}{12} \approx - 0.42$

$p = - 0.42$

2) $- \frac{1}{4} * \frac{2}{3} = q$

$q = - \frac{2}{12} = - \frac{1}{6} \approx - 0.17$ .

Therefore, a quadratic equation with roots $x_{1} = - 0.42$ and $x_{2} = - 0.17$ has the form:

$x^{2} - 0.42 x - 0.17 = 0$

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