You can solve quadratic equations with the p-q formula. Swedish National Test
Formula Collection
I hope you know that x^2 is the same as x²? Otherwise check "Skriva
Ma på dator"
(there is also described how you can write characters like ^ =
* / < > ( ) with a keyboard)
-5x^{2}
- 4x = - 9 is not in the right form: x² + px + q=0, What would make the x²
term not have - 5 as coefficient?
Divide both sides with - 5!
x^{2}
- 4x/(-5) = - 9/(-5) should have the signs sorted out and still doesn't have 0 in the right side (which fits the standard Swedish form).
DO NOT READ ANY MORE HINTS BEFORE YOU HAVE REALLY TRIED TO USE THE TIPS ABOVE AND TESTED YOUR ANSWER. But it you still aren't getting anywhere, look at more tips. There are about 13 all told.
x^{2}
+ 4x/5 = 9/5 after sorting out the signs according to (-a)/(-b) = + a/b, but we must get 9/5 out of the right side.
x^{2} + 4x/5
- 9/5 = 0 is in the form we want: x^2+px+q=0, but what are p and q?
+4x/5
= +(+4/5)x so one can see that p
must be +4/5 You can use 4/5 eller
.8 or 0.8 in your calculator or computer. What vill q be?
Is q = 9/5?
Uh uhhhh! No! Do not neglect our small friends, the minus signs! q = - 9/5 eller -1.8 is what it is!
When you are going to insert negative values into formulas surround them with parentheses until you see "whats what"!
x_{1} = -p/2 + sqrt((p^2)/(4) - q) is a "one-line" version of our quadratic equation root formula.
sqrt(something) (square
root) can be written just like in a spreadsheet (like Excel) (Swedish: eller sqrt(något)) in these numerical tutorial questions. You could also write it like a power instead. How?
square root can even be written as: (something)^(.5) or (something)^(1/2)
One root could be written as: -(4/5)/2 + sqrt((4/5)^2/4
- (-9/5))
NOTE: the sqrt expression MUST be held together with parentheses!
NOTE2: When you insert values inte formulas, have parentheses around them, especially if they are negative! Then you can calmly sort things out: - - and - + etc.
Note3: You can use your knowledge och signs to simplify the expression before you enter it into your calculator, computor or answer field (and 0 before the decimal point is not needed either):
If p is negative, you would need to use where> p is squared, since that will b ecome positive anyhow.
In this case q was negative so: -(-9/5) = + 9/5 so you can write one root as: -(4/5)/2 + rot((4/5)^2/4 + 9/5)
(On older calculators you may have to hit SQRT AFTER entering the parentheses contents.)
The other is gotten with: -(4/5)/2 -
rot((4/5)^2/4 + 9/5)
If you have a modern calculator you can simply get the other root by "backing into" the expression for the first root and replacing the + with - and hitting the ENTER, EXE
or = depending on what calculator. On Casio you can back in directly with the arrow buttons. On Texas you first hit 2^{nd}
and ENTER THEN you can go in with the arrows.
Casio often has a built-in quadratic equatuion solver EQUA>POLYNOMIAL>Degree
= 2.
You can write in a program in Texas that does the same thing. AndraGradsProgramTI81-82.PDF