quadratic formula

2014-08-22 8:58 am

considering the quadraric equation x^2-x/3=1
Angel uses a more complicated method
...but Jonathan uses a much quicker way. that is multiply both sides by 3.
then they are going to solve another equation:( x^2)/3-2x=3/5
if jonathan uses his own method as stated above, then what should be the first step of his calculation? (我想問個answer係咪兩边都乘15?)
and then try to solve the equation . (個answer係咪3+/-[(3root30)/5]

頭先的是情景題,依家返返黎正常d的 short questions :
solve the quadratic equations(leave the amswer in surd form)
1. (2x-1)^2=4x+3 (個answer係咪1+(root6)/2 但係er model answer 好似唔多似喎。)

2. 3x^2+10x-8=0

仲有想問关於presentation ge……
如果計到出黎係x=0 or x+3=0
我見d examples 寫左final solution. 係x=3
但係model answer 又寫0,3
我跟哪個呀?
謝謝!

回答 (1)

用戶26240

2014-08-22 10:41 am

✔ 最佳答案

Tosolve the equation (x²/3) - 2x = 3/5
Jonathan should firstly multiply both sides by 15.

That is :
(x²/3) - 2x = 3/5
[(x²/3) - 2x] * 15 = (3/5) * 15
5x² - 30x = 9
5x² - 30x - 9 = 0
x = [30 ± 6√(30² + 4*5*9)]/(2*5)
x = (15 + 3√30)/5 .or. x = (15 - 3√30)/5

=====
1.
(2x - 1)² = 4x + 3
4x² - 4x + 1 = 4x + 3
4x² - 8x - 2 = 0
2x² - 4x - 1 = 0
x = [4 ± √(4² + 4*2*1)]/(2*2)
x = (2 + √6)/2 .or. x = (2 - √6)/2

=====
2.
3x² + 10x - 8 = 0
(3x - 2)(x + 4) = 0
x= 2/3 .or. x = -4

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Question about presentation :

If x = 0 .or. x + 3 = 0
Then the solution is : x = 0 .or. x = -3

If x = 0 (rejected) .or. x + 3 = 0
Then the solution is : x = -3

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What isthe meaning of no real roots?

If both the two roots of a quadratic equation contain √(-1), represented as i,then the equation is said to be having no real roots.
The is because √(-1) is NOT a real number.

For example,
x² + 4 = 0
x² = -4
x² = ±√(-4)
x = ±2√(-1)
x = 2i .or. x = -2i

Then, the equation has no real roots.

參考: 土扁

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