solve the quadratic equation. 3x^2+9x_6=0
Answers
Step-by-step explanation:
(0 - 3x2) + 9x) - 6 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
-3x2 + 9x - 6 = -3 • (x2 - 3x + 2)
Trying to factor by splitting the middle term
3.2 Factoring x2 - 3x + 2
The first term is, x2 its coefficient is 1 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is +2
Step-1 : Multiply the coefficient of the first term by the constant 1 • 2 = 2
Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is -3 .
-2 + -1 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and -1
x2 - 2x - 1x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-2)
Add up the last 2 terms, pulling out common factors :
1 • (x-2)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-2)
Which is the desired factorization
Equation at the end of step
3
:
-3 • (x - 1) • (x - 2) = 0
STEP
4
:
Theory - Roots of a product
4.1 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.
Equations which are never true:
4.2 Solve : -3 = 0
This equation has no solution.
A a non-zero constant never equals zero.