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標題:
quadratic formula
發問:
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=3/5if jonathan uses his own method as stated above, then what should be the first step of his... 顯示更多 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! 更新: and whats the meaning of no real roots? 分唔到。
最佳解答:
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 ===== 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 ===== 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.
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