Question

If p = – 2, find the value of \[-3{{p}^{2}}+4p+7\]

Answer 1

Hint: First divide the required equation into 3 cases and then add them all together to get the required result. Assume the new variables for each of them and then find the value of each variable one by one. The Sum of these variables is our required result.

Complete step-by-step answer:
The given value of p in the question can be written as:
p = – 2…..(i)
The expression which we need to solve with this is:
\[-3{{p}^{2}}+4p+7\]
Let the value of this expression be assumed as L:
\[L=-3{{p}^{2}}+4p+7\]
Let the term \[-3{{p}^{2}}\] be assumed as variable ‘a’.
Let the term 4p be assumed as variable ‘b’.
Let the term 7 be assumed as variable ‘c’.
By substituting all these variables into the equation of L, we get,
L = a + b + c …..(ii)
Case 1: Solving for values of a, we take the equation (i) here. The value of p is given by the equation below:
p = – 2
By squaring on both the sides of the equation, we get it as:
\[{{p}^{2}}={{\left( -2 \right)}^{2}}\]
By simplifying, we can write it in the form
\[{{p}^{2}}=4\]
By multiplying – 3 on both the sides of the equation, we get it as
\[-3{{p}^{2}}=\left( -3 \right)\left( 4 \right)\]
By simplifying the above equation, we get the equation as
\[-3{{p}^{2}}=-12\]
By substituting it as variable ‘a’, we get a = – 12…..(iii)
Case 2: Solving for values of b, we take the equation (i) here. The value of p is given by the equation below:
p = – 2
By multiplying with 4 on both the sides of the equation, we get it as:
\[4p=\left( 4 \right)\left( -2 \right)\]
By simplifying, we can write it in the form
\[4p=-8\]
By substituting it as variable ‘b’, we get b = – 8…..(iv)
Case 3: Solving for values of c, as it is a constant, we write it directly. By our assumption, we get the value of c as
c = 7…..(v)
By adding equations (iii), (iv) and (v), we get the equation of the form:
a + b + c = – 12 – 8 + 7
By simplifying and substituting L, we get the value of L as
\[L=-13=-3{{p}^{2}}+4p+7\]
Therefore, the value of the expression given at p = – 2 is – 13.

Note: You can directly substitute and write the whole expression as one expression. We followed this method to increase the clarity while taking the value for b. Students generally forget the “ – “ sign and get the value as + 8. By this, the whole answer will be wrong. So, solve each and every step very carefully in order to get the exact result for the expression.