Evaluate \[{b^2} - 4ac\]for \[a = - 1\],\[b = - 5\]and \[c = 2\]?

Hint: In this question we have to find the value of the expression when \[a = - 1\],\[b = - 5\] and \[c = 2\], so we input the given value inside the given polynomial, thus substitute the values in place of \[a\], \[b\] and \[c\] in the polynomial given in the question and further simplification using the operations addition, subtraction and multiplication we will get the required value.

Complete step by step answer:
A polynomial is defined as an expression which is composed of variables, constants and exponents that are combined using the mathematical operations such as addition, subtraction, multiplication and division.
Given polynomial is \[{b^2} - 4ac\],
As the degree of the polynomial is 2 so, the polynomial is a quadratic polynomial.
We have to find the value of the given expression when \[a = - 1\],\[b = - 5\] and \[c = 2\], so substitute the values in place of\[a\], \[b\]and \[c\]in the given polynomial \[{b^2} - 4ac\], we get,
\[ \Rightarrow {b^2} - 4ac = {\left( { - 5} \right)^2} - 4\left( { - 1} \right)\left( 2 \right)\],
Now simplifying the right hand side by taking the square in the polynomial we get,
\[ \Rightarrow {b^2} - 4ac = 25 - 4\left( { - 1} \right)\left( 2 \right)\],
Now further simplification in the right hand side by taking out the brackets and multiplying we get,
\[ \Rightarrow {b^2} - 4ac = 25 + 8\],
Now adding for further simplification we get,
\[ \Rightarrow {b^2} - 4ac = 33\],
So, the value of the polynomial when \[a = - 1\], \[b = - 5\] and \[c = 2\] is 33.

\[\therefore \] The value of the expression \[{b^2} - 4ac\] when \[a = - 1\], \[b = - 5\] and \[c = 2\] is 36 will be equal to 33.

Note: To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.