The roots of 2x-2/x=3 are
Answers
Answer:
(2x2 - x) - 3 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 2x2-x-3
The first term is, 2x2 its coefficient is 2 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -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
2x2 - 3x + 2x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-3)
Add up the last 2 terms, pulling out common factors :
1 • (2x-3)
Step-5 : Add up the four terms of step 4 :
(x+1) • (2x-3)
Which is the desired factorization
Equation at the end of step
2
:
(2x - 3) • (x + 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-3 = 0
Add 3 to both sides of the equation :
2x = 3
Divide both sides of the equation by 2:
x = 3/2 = 1.500
Solving a Single Variable Equation:
3.3 Solve : x+1 = 0
Subtract 1 from both sides of the equation :
x = -1
Supplement : Solving Quadratic Equation Directly
Solving 2x2-x-3 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Step-by-step explanation:
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Answer:
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