Question

a student performed the following steps to find the solution to the equation x2+14x+45=0 where did the student go wrong? Step1: factor the polynomial into (x+5) and (x+9) step2: x+5=0 and x-9=0 step 3: x=-5 and x=9 A) in step 3 B) in step 2 C) in step 1 D) the student did not make any mistakes, the solution is correct.

Answer 1

x^2 + 14x + 45 = 0
(x + 5)(x + 9) = 0

x + 5 = 0
x = -5

x + 9 = 0 <=== here is the error...step 2
x = -9 

Answer 2

The student made mistake in step 2

The correct answer is an option (B)

What is an equation?

"It is a mathematical statement which consists of equal symbol between two mathematical expressions."

What is solution to an equation?

"It is a value of the variable which makes equation true."

For given question,

We have been given an equation $x^{2} +14x+45=0$

A student performed the following steps to find the solution to the equation $x^{2} +14x+45=0$

Step1: factor the polynomial into (x+5) and (x+9)

Step2: x+5=0 and x-9=0

Step 3: x=-5 and x=9

Now we solve given equation.

$\Rightarrow x^{2} +14x+45=0\\\\\Rightarrow x^{2} +9x+5x+45=0\\\\\Rightarrow x(x+9)+5(x+9)=0\\\\\Rightarrow (x+9)(x+5)=0\\\\\Rightarrow x+9=0~~and~~ x+5=0\\\\\Rightarrow x=-9~~and~~ x=-5$

We can observe that the student made mistake in step 2.

In stead of factor (x + 9), he wrote (x - 9)

Therefore, the student made mistake in step 2

the correct answer is an option (B)

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