Question

Determine the quadratic equation whose sum and product of the roots are 9 and 14 respectively

Answer 1

$\alpha + \beta = 9 \\ \\ \alpha \beta = 14 \\ \\ \\ so \\ \\ \\ \blue{\overbrace{ \: \: \underbrace{ \red{\boxed{ \orange{\sf{ {x}^{2} + ( \alpha + \beta )x - ( \alpha \beta ) } }}}} } } \\ \\ \\ \rm so \: \: \: the \: \: \: required \: \: \: quadratic \: \: \: polynomial \\ \\ \\ \rm is \: \: \: \: \boxed{ \sf {x}^{2} + 9x + 14}$

Answer 2

Given: The sum and product of the roots of a quadratic equation are 9 and 14, respectively.

To find: The quadratic equation.

Solution:

• Let the two roots of the equation be α and β.
• According to the question, the following two equations can be formed.

        $\alpha + \beta = 9$

        $\alpha \beta = 14$

• A quadratic equation with its roots can be represented as follows.

        $x^{2} + (\alpha +\beta )x + \alpha \beta = 0$

• on replacing the sum and the product of the roots with the terms in the given question, the equation obtained is as follows.

       $x^{2} + 9x + 14 = 0$

Therefore, the quadratic equation is x² + 9x + 14 = 0.