Question

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

where did the student go wrong?

Step 1. Factor the polynomial into (x + 5) and (x + 9)
Step 2. x + 5 = 0 or x - 9 = 0
Step 3. x = -5 or x = 9

a. in Step 2
b. in Step 3
c. The student did not make any mistakes, the solution is correct
d. in Step 1

Answer 1

The student made the mistake in step 2 while calculating the values of x ( option A)

The root of a quadratic equation can be found by using factorization method,

x² + 14x + 45 = 0

x² + 5x + 9x + 45 = 0

(x² + 5x )(+9x + 45) = 0

x(x +5) 9 ( x +5) = 0

(x + 9) ( x +5) = 0

step 2 should be ;

x+9 = 0

or x +5 = 0

But the student wrote x - 9 = 0 or x + 5 = 0

step 3 is x = -9 or -5

Therefore he made the mistake in step 2 by writing x - 9 instead of x +9