Question

How do you evaluate $\sqrt{{{b}^{2}}-4ac}$ for $a=1,b=12,c=11$ ?

Answer 1

Hint: We have given the values $a=1,b=12,c=11$ and we have to find the value of expression $\sqrt{{{b}^{2}}-4ac}$. We just substitute the given values in the expression and simplify the obtained expression by solving the operations like addition, subtraction, multiplication and division to get the desired answer.

Complete step by step answer:
We have been given the values $a=1,b=12,c=11$.
We have to evaluate the given expression $\sqrt{{{b}^{2}}-4ac}$.
We know that an expression contains variables, constants and algebraic operations. To solve an expression we need to substitute the value of variables and solve the operations given in the expression.
To evaluate the given expression we need to substitute the given values. Then we will get
\[\begin{align}
  & \Rightarrow \sqrt{{{b}^{2}}-4ac} \\
 & \Rightarrow \sqrt{{{12}^{2}}-4\times 1\times 11} \\
\end{align}\]
Now, simplifying the above obtained expression we will get
\[\Rightarrow \sqrt{144-44}\]
Now, subtracting the quantities inside the square root we will get
\[\Rightarrow \sqrt{100}\]
Now, we know that 10 is the square root of 100. So simplifying the above obtained square root we will get
\[\Rightarrow 10\]

Hence we get the value of the expression $\sqrt{{{b}^{2}}-4ac}$ as 10.

Note: The expression $\sqrt{{{b}^{2}}-4ac}$ is the part of the quadratic formula and is known as the discriminant of the quadratic equation. By evaluating the value of discriminate we can identify the nature of roots a quadratic equation has. In such types of questions be careful while substituting the values and while solving the expressions having more than two operators always follow BODMAS rule.