Question

Solve : ${{x}^{2}}-4x-21=0$

Answer 1

Hint: a quadratic equation is an equation where the maximum or highest degree of a variable cannot exceed $2$. In this question we have to find the value of $x$ from the given quadratic equation, to find the value of x we will factorise the given polynomial and thus find out results.

Complete step-by-step answer:
The given equation is : ${{x}^{2}}-4x-21=0$
Comparing the equation with standard quadratic equation $a{{x}^{2}}+bx+c=0$
We get the values of $a,b,c$ as,
$a=1$
$b=-4$
$c=-21$
we know that formula for solving quadratic equation is given as
$Dl=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$
Let us first find the value of discriminant where D= $\sqrt{{{b}^{2}}-4ac}$
substituting values of $a,b,c$ we get
$=\sqrt{{{\left( -4 \right)}^{2}}-4\left( 1 \right)\left( -21 \right)}$
on simplifying
$=\sqrt{16+84}=\sqrt{100}$
Substituting the value $\sqrt{{{b}^{2}}-4ac}$
$\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$
on solving ,
$x=\dfrac{4\pm 10}{2\left( 1 \right)}$
$x=\dfrac{4\pm 10}{2}$
Simplifying the above, we get
$x=\dfrac{4+10}{2},\dfrac{4-10}{2}$
$x=\dfrac{14}{2},\dfrac{-6}{2}$
$x=7,-3$

Hence, the required result the value of $x$ will be $7\And -3$

Additional Information:
Equation with the highest degree of variable $1$ is called a linear equation and only one value of variable is obtained and the standard form is given as $y=mx+c$.
Equation with the highest degree of variable 2 is called a quadratic equation and two values of variable is obtained and standard form is given as $a{{x}^{2}}+bx+c=0$.
There are different methods of factorisation such as grouping method, splitting the middle term.

Note:
Whenever there is a question where it is not compulsory to factorise using any specific method then you can apply any method as per your capability. The easiest method is splitting the middle term and then taking out common from it and thus calculating the value of the variable. To solve the given question which is difficult to split the equation them we need to find the solution by using quadratic formula $\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$.