x 1 x 2 x 3 x 4 24 0

x in [1, 2] uu [3, oo) f(x) = (x-1)(x-2)(x-3) = x^3-6x^2+11x-6 is a cubic with positive leading coefficient and zeros of multiplicity 1 at x=1, x=2 and x=3. As a result: f(x) is continuous. f(x) is positive for large positive values of x. f(x) is negative for large negative values of x. f(x) changes sign at each of its zeros. Hence f(x) is non-negative in the intervals [1, 2] and [3, oo) graph ( x ^2 - 1 ) ^3 - ( x ^4 x ^2 1 ) . ( x ^2 - 1 ) = 0. HOC24. Lớp học. Lớp học. Tất cả Lớp 12 Lớp 11 Lớp 10 Lớp 9 Lớp 8 Lớp 7 Lớp 6 Lớp 5 Lớp 4 Lớp 3 Lớp 2 Lớp 1 Hỏi đáp Đề thi Video bài giảng Khóa học Tin tức Cuộc thi vui Evay Vay Tiền. We have, \\frac{x-1x-2}{x-3x-4}\ ≥ 0 Equating x − 3x − 4 and x – 1x − 2 to zeto we obtain x = 3,4, 1, 2 as critical points. Plot these points on the real line as shown below. The real line is divided into 6 regions. When x > 4 ∴ \\frac{x-1x-2}{x-3x-4}\ ≥ 0 When 3 < x < 4 ∴ \\frac{x-1x-2}{x-3x-4}\ ≤ 0 When 2 ≤ x < 3 ∴ \\frac{x-1x-2}{x-3x-4}\ ≥ 0 When 1 ≤ ≤ 2 ∴ \\frac{x-1x-2}{x-3x-4}\ ≤ 0 When 1 < < 0 ∴ \\frac{x-1x-2}{x-3x-4}\ ≥ 0 When < 0 ∴ \\frac{x-1x-2}{x-3x-4}\≥ 0 Hence Solution Set, {−∞1] ∪ [2,34, ∞ Hence, solution set ≥ 4 ∈ [4, ∞ Algebra Examples Popular Problems Algebra Solve for x 4x-3-2x-1>0 Step 1Simplify .Tap for more steps...Step each for more steps...Step the distributive by .Step the distributive by .Step by adding for more steps...Step from .Step and .Step 2Add to both sides of the 3Divide each term in by and for more steps...Step each term in by .Step the left for more steps...Step the common factor of .Tap for more steps...Step the common by .Step the right for more steps...Step by .Step 4The result can be shown in multiple FormInterval Notation x={ 0, 5, 5/2+-sqrt15/2i } Let fx = x-1x-2x-3x-4 Then f0 = -1-2-3-4 = 4! = 24 f5 = 5-15-25-35-4 = 432*1 = 4! = 24 So both x=0 and x=5 are roots and x and x-5 are factors. fx-24 = x-1x-2x-3x-4-24 =x^4-10x^3+35x^2-50x =xx-5x^2-5x+10 The remaining quadratic factor is in the form ax^2+bx+c, with a=1, b=-5 and c=10. This has zeros given by the quadratic formula x = -b+-sqrtb^2-4ac/2a =5+-sqrt5^2-4110/2 =5+-sqrt-15/2 =5/2+-sqrt15/2i Question AZero is one of the roots of the equationBThe given equation has no rootsCThe given equation has exactly rootsDThe given equation is an identityEasyOpen in AppSolutionVerified by TopprCorrect option is A or When multiplied, the constant term 24 will be cancelled and x will become a common factor and, hence, will be one of the this answer helpful? 00

x 1 x 2 x 3 x 4 24 0