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What is the 64 time table?
1x64=64 2x64=128 3x64=192 4x64=256 5x64=320 6x64=384 7x64=448 8x64=512 9x64=576 10x64=640 11x64=704 12x64=768
Y equals 20x3-15x plus 6x-2?
y = 20x3 - 15x + 6x - 2 ory = 20x3 - 9x - 2Plot the graph of y = 20x3 - 9x - 2 in the window [-1, 1] by [-2, 1] in your graphing calculator..Use 2ND/CALC/zero to find the x-intercept values which are the zeros of the function such asx ≈ 0.76x ≈ -0.26x ≈ -0.5If the equation is y = 20x3 - 15x2 + 6x - 2, then from the Descartes' rule of sign we have:f(x) = 20x3 - 15x2 + 6x - 2 (two changes in sign, so there are two or one positive real zeros)f(-x) = -20x3 - 15x2 - 6x - 2 (no changes in sign, there is any negative real zero)Since there are three zeros (degree of 3), we must have only one real positive zero, and two conjugate complex zeros.When you plot the graph of y = 20x3 - 15x2 + 6x - 2 in the same window as above, you find that the real zero is x ≈ 0.5 = 1/2.The sum of the roots = - -15/20 = 3/4 [-(the coefficient of x2/the coefficient of x3]The product of the roots = - -2/20 = 1/10 [odd degree -(the constant//the coefficient of x3]Let the complex roots be a + bi and a - bi, then we have:1/2 + a + bi + a - bi = 3/42a = 3/4 - 1/22a = 1/4a = 1/8 = 0.125(1/2)(a + bi)(a - bi) = 1/10(1/2)(a2 - b2i2) = 1/10 (substitute -1 for i2)a2 + b2 = 1/10 ÷ 1/2 (substitute 1/8 for a)(1/8)2 + b2 = 1/10 x 2/11/64 + b2 = 1/5b2 = 1/5 - 1/64b2 = 1x64/5x64 - 1x5/64x5 = 64/320 - 5/320 = 59/320b = ± √(59/320) ≈ ± 0.4So that a + bi = 0.125 + 0.4i, a - bi = 0.125 - 0.4iThus the zeros are 0.5, 0.125 + 0.4i, and 0.125 - 0.4i.
