Answer:
{1, (-1±√17)/2}
Step-by-step explanation:
There are formulas for the real and/or complex roots of a cubic, but they are so complicated that they are rarely used. Instead, various other strategies are employed. My favorite is the simplest--let a graphing calculator show you the zeros.
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Descartes observed that the sign changes in the coefficients can tell you the number of real roots. This expression has two sign changes (+-+), so has 0 or 2 positive real roots. If the odd-degree terms have their signs changed, there is only one sign change (-++), so one negative real root.
It can also be informative to add the coefficients in both cases--as is, and with the odd-degree term signs changed. Here, the sum is zero in the first case, so we know immediately that x=1 is a zero of the expression. That is sufficient to help us reduce the problem to finding the zeros of the remaining quadratic factor.
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Using synthetic division (or polynomial long division) to factor out x-1 (after removing the common factor of 4), we find the remaining quadratic factor to be x²+x-4.
The zeros of this quadratic factor can be found using the quadratic formula:
a=1, b=1, c=-4
x = (-b±√(b²-4ac))/(2a) = (-1±√1+16)/2
x = (-1 ±√17)2
The zeros are 1 and (-1±√17)/2.
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The graph shows the zeros of the expression. It also shows the quadratic after dividing out the factor (x-1). The vertex of that quadratic can be used to find the remaining solutions exactly: -0.5 ± √4.25.
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The given expression factors as ...
4(x -1)(x² +x -4)
Answer:
step by step:
3x+5=-2
move constant to the right-hand side and change it's sign
3x=-2-5
Calculate the difference
3x=-7
Divided both sides of the equation by 3
Answer:
9.07571212
Step-by-step explanation:
To solve this we first need to find the area of the circle, r squared times pi
4 x 4 x pi = 50.2654825
Now we multiply this by 65/360, 50.2654825 x 65/360 = 9.07571212
The shaded sector covers 9.07571212 square inches.
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Forces in direction x:
fx1 = 100 * cos (50) = 64.28
fx2 = 50 * cos (160) = - 46.99
The resultant is:
fx = fx1 + fx2 = 17.29
Forces in direction y:
fy1 = 100 * sine (50) = 76.60
fy2 = 50 * sine (160) = 17.10
The resultant is:
fy = fy1 + fy2 = 93.70
The magnitude of the resulting force is:
f = root (fx ^ 2 + fy ^ 2)
f = root ((17.29) ^ 2 + (93.70) ^ 2)
f = 95.28
The angle is:
theta = atan (fy / fx)
theta = atan (93.70 / 17.29)
theta = 79.55 degrees
Answer:
The direction and magnitude of the resultant force are:
f = 95.28 pounds at theta = 79.55 degrees