Ex.14.3 Q13 Factorization - NCERT Maths Class 8

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Question

Q13. Find and correct the errors in the following mathematical statement.

Substituting \(x = - 3\) in

(a)\(\begin{align}\quad{x^2} + 5x + 4\;\;{\rm{gives}}\;\;{{( - 3)}^2} + 5( - 3) + 4 = 9 + 2 + 4 = 15\end{align}\)

(b)\(\begin{align}\quad{x^2} - 5x + 4\;\;{\rm{gives}}\;\;{{( - 3)}^2} - 5( - 3) + 4 = 9 - 15 + 4 = - 2\end{align}\)

(c)\(\begin{align}\quad{x^2} + 5x\;\;{\rm{gives}}\;\;{{( - 3)}^2} + 5( - 3) = - 9 - 15 = - 24\end{align}\)

Text Solution

What is known?

Incorrect mathematical statement.

What is unknown?

Correct mathematical statement.

Reasoning:

Put value of \(x\) in \(L.H.S\) and find correct solution.

Steps:

(a) For \(x = -\, 3\)

\[\begin{align}L.H.S = {x^2} + 5x + 4 &= {( - 3)^2} + 5( - 3) + 4\\&= 9 - 15 + 4\\& = 13 - 15\\& =  - 2\\L.H.S &\ne R.H.S\\{\text{The correct statement is }}{x^2} + 5x + 4 &=  - 2\\\end{align}\]

(b) For \(x = -\, 3\)

\[\begin{align}{{\text{(b) }}\;{\rm{For }}\,\,x =  - 3}\\{x^2} - 5x + 4 &= {( - 3)^2} - 5( - 3) + 4\\& = 9 + 15 + 4\\&= 28\\{\text{The correct statement is }}{x^2} - 5x + 4 = 28\\\end{align}\]

(c) For \(x = - 3\)

\[\begin{align}{x^2} + 5x & = {( - 3)^2} + 5( - 3)\\& = 9 - 15\\&  =  - 6\\{\text{The correct statement is }}{x^2} + 5x =  - 6\end{align}\]