![]() ![]() These are the cubic and quartic formulas. There are general formulas for 3rd degree and 4th degree polynomials as well. Similar to how a second degree polynomial is called a quadratic polynomial. A third degree polynomial is called a cubic polynomial. A trinomial is a polynomial with 3 terms. 2 − 10 2 \frac 2 2 1 0 start fraction, 2, plus, square root of, 10, end square root, divided by, 2, end fractionįirst note, a "trinomial" is not necessarily a third degree polynomial. If asked for the exact answer (as usually happens) and the square roots can’t be easily simplified, keep the square roots in the answer, e.g. If you use a calculator, the answer might be rounded to a certain number of decimal places.Keep the / − /- / − plus, slash, minus and always be on the look out for TWO solutions.Watch your negatives: b 2 b^2 b 2 b, squared can’t be negative, so if b b b b starts as negative, make sure it changes to a positive since the square of a negative or a positive is a positive. ![]() Make sure you take the square root of the whole ( b 2 − 4 a c ) (b^2 - 4ac) ( b 2 − 4 a c ) left parenthesis, b, squared, minus, 4, a, c, right parenthesis, and that 2 a 2a 2 a 2, a is the denominator of everything above it.Be careful that the equation is arranged in the right form: a x 2 b x c = 0 ax^2 bx c = 0 a x 2 b x c = 0 a, x, squared, plus, b, x, plus, c, equals, 0 or it won’t work!.Goal : To solve the quadratic equation, make it square. Square is beautiful so we can easily get the answer. To make rectangle, coefficient of X square should be 1.Īs we already know, the area of our shapes is big square minus small square.Īs you already know, to solve the quadratic equation we should make a rectangle to square. X is -2 and -4 Proof of quadratic formula ![]() Area of big square with (X 3) minus area of small square with 3. We can calculate the area of our shape in another perspective. Please do not forget the area of our shape still X(X 6). The shape that we made is part of that square. Look at the shape with birds eye, you can find beautiful square with each side measuring (X 3). It just cut and paste, so the area of the shape still x(x 6). Cut the rectangle in right half and paste it below the left rectangle. You can imagine anything and everything is possible in math, as a great mathematician find "imaginary number". Good Question!! But it's very difficult question for me(my major is not math). Some one might ask "how the area of rectangle can be negative?". You can find the rectangle that has a length of (x 6) and a width of x. If using factorization, we can easily find the solution. ![]() If you divided the 1 big rectangle to small 4 rectangles, you can find the area of big rectangle is same as sum of 4 small rectangles area. To find the area of a rectangle, multiply the length by the width. We can use the distributive law like this.Īlso the equation is converted to "area of a rectangle" that has a length of (a b) and a width of (c d). Using shapes is very useful to remember how to solve the quadratic equation even though I forget the formula. In this article, I tried to proof quadratic formula that I already forgot, despite I used more than tens of times at school days. Doing that we also get new aspect of the equations and find new idea. One of the interesting things when learning Math is we can convert equations to shapes or graphs. I got the idea from ( ) to write this article. ![]()
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