二次方程的求根公式(Quadratic Formula)是用于求解形如( ax^2 + bx + c = 0 )(( a \neq 0 ))的方程根的关键工具。其核心表达式为( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ),通过代入系数( a )、( b )、( c )可计算方程的实数或复数解。以下从公式结构...
Wherea,b,andcarerealnumbersanda0 Soifwehaveanequationinxandthehighestpoweris2,itisquadratic.Tosolveaquadraticequationwegetitintheformaboveandseeifitwillfactor.x5x6 2 Getformabovebysubtracting5xandadding6tobothsidestoget0onrightside.-5x+6 -5x+6 Factor.UsetheNullFactorlawandseteachfactor=0...
( 6x^2-4-5x=0) Use the quadratic formula to find the solutions. ( (-b± √(b^2-4(ac)))/(2a)) Substitute the values ( a=6), ( b=-5), and ( c=-4) into the quadratic formula and solve for ( x). ( (5± √(((-5))^2-4⋅ (6⋅ -4)))/(2⋅ 6)) Simpli...
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Example: Solve 5x2 + 6x + 1 = 0 Coefficients are:a = 5, b = 6, c = 1 Quadratic Formula:x = −b ±√(b2 − 4ac) 2a Put in a, b and c:x = −6 ±√(62 − 4×5×1) 2×5 Solve:x = −6 ±√(36− 20) 10 x = −6 ±√(16) 10 x = −6 ...
Solve using the quadratic formula: 4x2 + 4x + 1 = 0 9. MULTIPLE CHOICE 1 min • 1 pt Use the quadratic formula to find the solutions for y = -x2 - 5x + 12 10. MULTIPLE CHOICE 5 mins • 1 pt What are the solutions of a2=6a+3a2=6a+3 ? 使用免费帐户探索所有问题继续使用 ...
Let's guess (2x+3)(x+1): (2x+3)(x+1) = 2x2 + 2x + 3x + 3 = 2x2 + 5x + 3 (Close but WRONG) How about (2x+7)(x−1): (2x+7)(x−1) = 2x2 − 2x + 7x − 7 = 2x2 + 5x − 7 (WRONG AGAIN) OK, how about (2x+9)(x−1): (2x+9)(x−1) ...
2. Multiple Choice 5 mins 1 pt Use the quadratic formula to solve 2x2 + 2x - 12? -2, 3 2, 3 2, -3 -2, -3 3. Multiple Choice 5 mins 1 pt In the equation y = x2 +5x +7, match each leading coefficient with its correct letter a=0, b=5, c=7 a=1, b=5, c...
x=4.5, -4.5 4x² - 81=0 x= -1, 2.5 2x² +2x = 5 +5x x= -1/3, 2.5 10= 6x² -13x +5 x = -1/2, -3/5 10x² + 11x + 3 = 0 x=1, -1 x² +3x = 3x + 1 x= 6, -6 2x² - 72=0 x= -4, 4 ...
= -(x2 - 5x -36) = -x2 + 5x + 36 (2). y = 3(x -1)2 + 8 = 3(x -1)(x - 1) + 8 = 3(x2 - x - x + 1) + 8 = 3(x2 - 2x + 1) + 8 = 3x2 - 6x + 3 + 8 = 3x2 - 6x + 11 QUADRATIC FUNCTIONS IN REAL LIFE ...