Question

How do you solve ${x^2} - 20 = 0?$ ?

Answer 1

Hint: Use quadratic equation formula to solve the equation.
Quadratic equation: Quadratic equations are the polynomial equations of degree two in one variable. The degree of the polynomial is the highest power of the variable in the equation. The general form of quadratic equation is $f\left( x \right) = a{x^2} + bx + c$ where $a,b$ and $c$, belongs to real numbers and the coefficients of the ${x^2}$ is known as leading coefficient and $c$ is called constant absolute term of $f\left( x \right)$.
The values of $x$ satisfying the quadratic equation are the roots of the quadratic equation.
A quadratic equation will always have two roots. The nature of roots can be either real or imaginary.
A quadratic polynomial, when equated to zero becomes a quadratic equation.
A quadratic equation becomes an identity $\left( {a,b,c = 0} \right)$ if the equation is satisfied by more than two numbers, having more than two roots or solutions either real or complex.

Formula Used: Formula for finding the roots of quadratic equation is,
$\left( {m,n} \right) = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$
Where m and n are the roots of the quadratic equation,
$f\left( x \right) = a{x^2} + bx + c$.

Complete step-by-step answer:
Step: 1 Compare the equation ${x^2} - 20 = 0$ with the quadratic equation $f\left( x \right) = a{x^2} + bx + c$.
$
   \Rightarrow a = 1 \\
   \Rightarrow b = 0 \\
   \Rightarrow c = - 20 \\
 $
Substitute the values in the formula to find the root of the equation.
Suppose $\left( {m,n} \right)$are roots of the equation.
$
  \left( {m,n} \right) = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} \\
   \Rightarrow \left( {m,n} \right) = \dfrac{{ - 0 \pm \sqrt {0 - 4 \times 1 \times \left( { - 20} \right)} }}{{2 \times 1}} \\
   \Rightarrow \left( {m,n} \right) = \pm \sqrt {20} \\
 $

Therefore the roots of the quadratic equations are $ \pm \sqrt {20} $.

Note:
Students must remember the formula to find roots of the quadratic equation.
They must compare the given quadratic equation with the general form of quadratic equation and find the values of the respective coefficients. Students are advised to not make any mistake in writing the formula of quadratic equations. Students should use an alternative method to find the solutions.
Alternative method:
The equation is ${x^2} - 20 = 0$.