Product of the Solutions of a Quadratic Equation
Example corresponding to question 7 in algebra_1.
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Example 1
What is the product of the solutions of the equation $− 3 x^2 = − 17$ ?
- $\dfrac{17}{3}$
- $51$
- $-51$
- $-\dfrac{17}{3}$
- $-17$
Solution
This example is about finding the product of the Solutions of a quadratic equation.
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The given equation can be written as $3 x^2 - 17=0$ which is a quadratic equation. There are two ways in finding the product of the solutions of this equation.
1) We solve
$x^2 = \dfrac{17}{3}$
Solutions: $x = \sqrt{\dfrac{17}{3}}$ and $x = -\sqrt{\dfrac{17}{3}}$
The product is $\sqrt{\dfrac{17}{3}} \times -\sqrt{\dfrac{17}{3}} = - \dfrac{17}{3}$
2) We may also use the formula for the product of the solutions of a quadratic equation of the form $ax^2+bx+c=0$ which is $\dfrac{c}{a}$. In the given equation $3 x^2 - 17=0$, $c=-17$ and $a=3$. Hence
$\dfrac{c}{a}=-\dfrac{17}{3}$
Answer D
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