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About Josh
Expertise
When I work through problems, I emphasize principles and key ideas which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponentials & Logarithms. Basic Calculus. Probability, Permutations and Combinations. Mathematical Induction. Complex numbers. Physics problems.
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Experience:
I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.
Supplementary Website:
See a selection of past questions in my maths repository under "Question Archive"
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Bachelor degree in Engineering Science.
"Everyone struggles with something."
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You are here: Experts > Science > Math for Kids > Basic Math > quadratics
Expert: Josh - 10/7/2008
Question
hey there would really appriciatie you taking the time to help me. the question states:3x^2-4=0 express your answer in simplest radical form. dont know if i should use the formula or complete the square as i am not good with factoring, also have another question how do i factor the following equation 3x^2-6.thank you very much
Answer
Hi Nabeel,
Generally speaking, we should use the quadratic formula
x=[-b+sqrt(b*b-4ac)]/(2a),[-b-sqrt(b*b-4ac)]/(2a)
only as our last resort.
with the 1st expression, the first step we should take is to separate the known "4" from the unknown "3x^2".
Adding 4 to both sides of the equation 3x^2-4=0, we have 3x^2=4.
Dividing both sides by 3, we get x^2=(4/3). Finally, taking the square root on both sides, we get x=2/sqrt(3) or -2/sqrt(3).
If we can spot a common factor in the expression, it's best to factorize it because the answer will soon become obvious.
e.g., with the second expression, 3x^2-6, notice that both terms (3x^2 and 6) are divisible by 3. So, we can pull the "3" out and treat it as a common factor. since 3x^2= 3*(x^2) and -6 = 3*(-2), we have 3x^2-6 = 3(x^2-2) that's how we factorize.
If you are asked to solve 3x^2-6=0, finding the solution to 3x^2-6=0 is equivalent to solving 3(x^2-2)=0. Using the square of difference result [x^2-a^2 = (x+a)(x-a), this holds for any real number a] we have 3(x+sqrt(2))(x-sqrt(2))=0
Remember that we are multiplying three terms on the left hand side (LHS). The LHS of the equation equals the RHS (zero)
if x+sqrt(2)=0, i.e., x=-sqrt(2) OR
if x-sqrt(2)=0, i.e., x=+sqrt(2).
So, the solutions are x=sqrt(2),-sqrt(2).
Another way to solve this is like the first example we've seen. First, separate the known from the unknown.
3x^2-6=0 becomes 3x^2=6.
Then, divide throughout by 3. We get x^2=2.
Finally, taking the square root on both sides, x=sqrt(2) or -sqrt(2).
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