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 explanation:
it 28 by adding 6 +1 is 7 and times it by 4
Answer:
1. A) -12, 3 B) -6, 9 C) 0, -6 D) -15, -6
2. L) 1, -4 M) 6, 4 N) 7, -2
3. P) 4, 12 Q) 12, 12 R) 12, 8 S) 4, 8
4. W) 3, -6 X) 9, -3 Y) 15, -6 Z) 9, -9
5. M) -14, -8 N) -8, -6 O) -6, -12 P) -12, -14
6. D) -1, 3 E) 2, 2 F) 2, 1 G) -1, 0
Answer:
same as other answer
Step-by-step explanation:
According to the definition, is a parabola is in the standard form of (x-h)^2<span>=4p(y-k), then the directrix is y=k-p. In this case, the parabola function is x^2=8y, so h=0, p=8/4=2, k=0. Plug the values of h, p, k, into y=k-p, the directrix is y=-2.</span>