Find the roots of the quadratic equation. 6m²-m-2=0
Answers
Answer:
PLZZ follow me ❤️❤️
2.1 Factoring 6m2-m-2
The first term is, 6m2 its coefficient is 6 .
The middle term is, -m its coefficient is -1 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 6 • -2 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .
-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3
6m2 - 4m + 3m - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
2m • (3m-2)
Add up the last 2 terms, pulling out common factors :
1 • (3m-2)
Step-5 : Add up the four terms of step 4 :
(2m+1) • (3m-2)
Which is the desired factorization
Answer:
Step by Step Solution:
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "m2" was replaced by "m^2".
Step by step solution :
STEP
1
:
Equation at the end of step 1
((2•3m2) - m) - 2 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 6m2-m-2
The first term is, 6m2 its coefficient is 6 .
The middle term is, -m its coefficient is -1 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 6 • -2 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .
-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3
6m2 - 4m + 3m - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
2m • (3m-2)
Add up the last 2 terms, pulling out common factors :
1 • (3m-2)
Step-5 : Add up the four terms of step 4 :
(2m+1) • (3m-2)
Which is the desired factorization
Equation at the end of step
2
:
(3m - 2) • (2m + 1) = 0
STEP
3
:
Theory - Roots of a product
3.1 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.
Solving a Single Variable Equation:
3.2 Solve : 3m-2 = 0
Add 2 to both sides of the equation :
3m = 2
Divide both sides of the equation by 3:
m = 2/3 = 0.667
Solving a Single Variable Equation:
3.3 Solve : 2m+1 = 0
Subtract 1 from both sides of the equation :
2m = -1
Divide both sides of the equation by 2:
m = -1/2 = -0.500