Find and explain the error in the student’s work/answers below.
Solve: m² + m – 6 = 0
m² – 2m + 3m – 6 = 0
m(m – 2) + 3(m – 2) = 0
(m – 2)(m + 3) = 0
m – 2 = 0 or m + 3 = 0
m = –2 or m = 3
The error is in line 2 where the student incorrectly rewrites the equation. The correct way to rewrite the equation would be: m² + m – 6 = 0, which is the original equation given. The student should not have added 3m and then subtracted 2m to the equation. This mistake leads to an incorrect factorization in line 3 and ultimately incorrect solutions in the final step.
m – 2 = 0 or m + 3 = 0
********** m = –2 or m = 3 *********
NO
m = +2 or m = -3
=========================
check
==========================
m² + m – 6 = 0
if m = -2
4 +2- 6 = 0 yes
if m = -3
9 - 3 - 6 = 0 yes
The revised answer with the correct solutions (m = 2 or m = -3) and correct check is correct.
The error in the student's work is in the step where they factored the equation incorrectly. Let's break down the correct factoring process:
Starting with the quadratic equation: m² + m - 6 = 0
We want to rewrite the middle term, which is "m", as the sum of two terms whose coefficients multiply to give the product of the square term (m²) and the constant term (-6). In this case, we need to find two numbers whose product is -6 and whose sum is 1 (coefficient of the middle term, m). These numbers are -2 and 3.
So, the correct factoring step should be:
m² - 2m + 3m - 6 = 0
Now, we group the terms:
(m² - 2m) + (3m - 6) = 0
Next, we factor out the common terms from each group:
m(m - 2) + 3(m - 2) = 0
And finally, we notice that we have a common binomial, (m - 2), which we can factor out:
(m - 2)(m + 3) = 0
Now we can set each factor to zero and solve for m:
m - 2 = 0 or m + 3 = 0
Solving these equations, we find:
m = 2 or m = -3
Therefore, the correct solutions to the quadratic equation are m = 2 and m = -3.