Question

If $ a = 1 $ , $ b = 8 $ and $ c = 15 $ , then find the value of $ {b^2} - 4ac $ ?

Answer 1

Hint: We are required to find the value of an expression for a certain value of the variables otr unknowns. This question requires us to have the knowledge of basic and simple algebraic rules and operations such as substitution, addition, multiplication, subtraction and many more like these. A thorough understanding of algebraic expressions, functions and applications can be of great significance.

Complete step-by-step answer:
In the given question, we are required to find the value of an algebraic expression for a certain value of variable. The value of an expression at a certain value of variable or unknown is found by substituting the value of variable as specified in the question into the expression.
So, the algebraic expression given to us in the question is $ {b^2} - 4ac $ .
The value of a that we have to put in the expression is $ 1 $ .
The value of b to be put into the expression is $ 8 $ .
The value of c to be put in the expression is $ 15 $ .
So, we need to replace the variable in the expression given to us in the question by the values of the unknowns specified.
So, we have, $ {b^2} - 4ac $
Substituting the values of a, b and c, we get,
 $ \Rightarrow {\left( 8 \right)^2} - 4\left( 1 \right)\left( {15} \right) $
Evaluating the square of $ 8 $ and simplifying the expression, we get,
 $ \Rightarrow 64 - 60 $
 $ \Rightarrow 4 $
Hence, we get the value of the required expression $ {b^2} - 4ac $ as $ 4 $ by replacing the values of a, b and c as $ 1 $ , $ 8 $ , and $ 15 $ .
So, the correct answer is “4”.

Note: Such questions that require just simple change of variable can be solved easily by keeping in mind the algebraic rules such as substitution and transposition. Substitution of a variable involves putting a certain value in place of the variable. That specified value may be a certain number or even any other variable.