Step-by-step explanation:
they're is a neat little trick.
but first of all, "roots" means the 0 solutions of the equation. like
ax² + bx + c = 0
there are 2 solutions for x to make the whole expression equal 0.
these are the "roots".
now to the little trick :
when is a multiplication resulting in 0 ?
when at least one of the factors is 0.
and any quadratic expression can be written as multiplication of 2 factors. like
c(x - a)(x - b) = cx² - cax - cbx + cab
what are the "roots" or 0 points ?
either
c = 0
x - a = 0 | x = a
x - b = 0 | x = b
the leading coefficient = 3.
that means nothing else than c = 3.
root = 1 means (x - 1) is one factor.
root = -5 means (x + 5) is the other factor.
so, we have
3(x - 1)(x + 5) = 3x² + 12x - 15
and the equation is
3x² + 12x - 15 = 0
or
3x² + 12x = 15
Adding Integers
If the numbers that you are adding have the same sign, then add the numbers and keep the sign.
Example:
-5 + (-6) = -11
Adding Numbers with Different Signs
If the numbers that you are adding have different (opposite) signs, then SUBTRACT the numbers and take the sign of the number with the largest absolute value.
Examples:
-6 + 5= -1
12 + (-4) = 8
Subtracting Integers
When subtracting integers, I use one main rule and that is to rewrite the subtracting problem as an addition problem. Then use the addition rules.
When you subtract, you are really adding the opposite, so I use theKeep-Change-Change rule.
The Keep-Change-Change rule means:
Keep the first number the same.
Change the minus sign to a plus sign.
Change the sign of the second number to its opposite.
Example:
12 - (-5) =
12 + 5 = 17
Multiplying and Dividing Integers
The great thing about multiplying and dividing integers is that there is two rules and they apply to both multiplication and division!
Again, you must analyze the signs of the numbers that you are multiplying or dividing.
The rules are:
If the signs are the same, then the answer is positive.
If the signs are different, then then answer is negative.
There is no solution ,<span>a+c=-10;b-c=15;a-2b+c=-5 </span>No solution System of Linear Equations entered : [1] 2a+c=-10
[2] b-c=15
[3] a-2b+c=-5
Equations Simplified or Rearranged :<span><span> [1] 2a + c = -10
</span><span> [2] - c + b = 15
</span><span> [3] a + c - 2b = -5
</span></span>Solve by Substitution :
// Solve equation [3] for the variable c
<span> [3] c = -a + 2b - 5
</span>
// Plug this in for variable c in equation [1]
<span><span> [1] 2a + (-a +2?-5) = -10
</span><span> [1] a = -5
</span></span>
// Plug this in for variable c in equation [2]
<span><span> [2] - (-? +2b-5) + b = 15
</span><span> [2] - b = 10
</span></span>
// Solve equation [2] for the variable ?
<span> [2] ? = b + 10
</span>
// Plug this in for variable ? in equation [1]
<span><span> [1] (? +10) = -5
</span><span> [1] 0 = -15 => NO solution
</span></span><span>No solution</span>
You need the Least Common Multiple of 12 and 9.
That's 36.
3 x 12 = 36
4 x 9 = 36
Answer:
of what?
Step-by-step explanation: