find root and product 6x²-x-1=0
Answers
Answer:
Step-by-step explanation:
((2•3x2) - x) - 1 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 6x2-x-1
The first term is, 6x2 its coefficient is 6 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -1
Step-1 : Multiply the coefficient of the first term by the constant 6 • -1 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -1 .
-6 + 1 = -5
-3 + 2 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 2
6x2 - 3x + 2x - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (2x-1)
Add up the last 2 terms, pulling out common factors :
1 • (2x-1)
Step-5 : Add up the four terms of step 4 :
(3x+1) • (2x-1)
Which is the desired factorization
Equation at the end of step
2
:
(2x - 1) • (3x + 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 : 2x-1 = 0
Add 1 to both sides of the equation :
2x = 1
Divide both sides of the equation by 2:
x = 1/2 = 0.500
Solving a Single Variable Equation:
3.3 Solve : 3x+1 = 0
Subtract 1 from both sides of the equation :
3x = -1
Divide both sides of the equation by 3:
x = -1/3 = -0.333
Supplement : Solving Quadratic Equa