Question

Write The Quadratic Equation Whose Roots Are $2$ And $3$.

Answer 1

Determine the Quadratic Equation using relation between roots and coefficients

Quadratic equations are second-degree algebraic expressions and are of the form $a{x}^2+bx+c=0$.

The Standard form of quadratic equation with roots ‘$m$’ and ‘$n$ is $x^2–(m+n)x+mn=0$

Given root are $2$ And $3$, so

$$\begin{gathered} m=2 \\ n=3 \end{gathered}$$

Calculate the sum of the roots:

$$\begin{gathered} m+n=2+3 \\ =5 \end{gathered}$$

Calculate the product of the roots:

$\begin{array}{rcl}m\times n& =& 2\times 3\\ & =& 6\end{array}$

Putting the value sum and product root value into the standard quadratic equation:

$$\begin{gathered} x^2–(m+n)x+mn=0 \\ \Rightarrow x^2–\left(5\right)x+6=0 \\ \Rightarrow x^2–5x+6=0 \end{gathered}$$

Hence, the quadratic equation is $x^2–5x+6=0$.