3x²-7x-6 express in minus of two roots
Answers
hey
STEP
1
:
Equation at the end of step 1
(3x2 - 7x) - 6 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 3x2-7x-6
The first term is, 3x2 its coefficient is 3 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 3 • -6 = -18
Step-2 : Find two factors of -18 whose sum equals the coefficient of the middle term, which is -7 .
-18 + 1 = -17
-9 + 2 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 2
3x2 - 9x + 2x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (x-3)
Add up the last 2 terms, pulling out common factors :
2 • (x-3)
Step-5 : Add up the four terms of step 4 :
(3x+2) • (x-3)
Which is the desired factorization
Equation at the end of step
2
:
(x - 3) • (3x + 2) = 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.
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