Product of the Solutions of a Quadratic Equation

Example corresponding to question 7 in algebra_1.

Example 1


What is the product of the solutions of the equation $− 3 x^2 = − 17$ ?

  1. $\dfrac{17}{3}$

  2. $51$

  3. $-51$

  4. $-\dfrac{17}{3}$

  5. $-17$

Solution

This example is about finding the product of the Solutions of a quadratic equation.

  1. 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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