9) The roots of equation
m² + 7m = 0
Answers
Answer:
m(m+7) =0
m=0 or m+7=0 i. e. m=-7
Answer:
Changes made to your input should not affect the solution:
(1): "m2" was replaced by "m^2".
Step by step solution :
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring m2-7m-60
The first term is, m2 its coefficient is 1 .
The middle term is, -7m its coefficient is -7 .
The last term, "the constant", is -60
Step-1 : Multiply the coefficient of the first term by the constant 1 • -60 = -60
Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is -7 .
-60 + 1 = -59
-30 + 2 = -28
-20 + 3 = -17
-15 + 4 = -11
-12 + 5 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 5
m2 - 12m + 5m - 60
Step-4 : Add up the first 2 terms, pulling out like factors :
m • (m-12)
Add up the last 2 terms, pulling out common factors :
5 • (m-12)
Step-5 : Add up the four terms of step 4 :
(m+5) • (m-12)
Which is the desired factorization
Equation at the end of step
1
:
(m + 5) • (m - 12) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Step-by-step explanation:
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