If the equation has real coefficients, and 5 - i is a root, then its conjugate, 5 + i must be a root.
Since 5 - i and 5 + i are roots, then (x - 5 + i) and (x - 5 - i) are factors.
That means x2 - 10x + 26 is a factor.
The other root is x = -3 so x + 3 is the other factor.
So the cubic is (x + 3)*(x2 - 10x + 26) = 0
That is x3 - 7x2 - 4x + 78 = 0
the integral of the square-root of (x-1)2 = x2/2 - x + C
A polynomial function is defined for all x, ranging from minus infinity to plus infinity. Since it is defined for all x, it is defined for x = 0 and this is the point where it intersects the y-axis which is called the y-intercept. It is possible, with suitable choice of coefficients that the function is always positive or always negative. In either case it will not cross the x-axis so that there is no x-intercept. However, it is not true to say that all polynomial functions with real coefficients do not have an x-intercept. In fact all polynomials of odd order (linear, cubic, quintic etc) will have at least one x-intercept.
You would need to know what a is equal to in order to calculate this equation.
It is a linear equation in two variables
Without any equality and not knowing the plus or minus values of 1 and 45 it is not an equation so therefore it has no solution.
If it has integral coefficients and 4+i is a root then its conjugate, 4-i must also be a root. So the equation is f(x) = (x-2)*(x-4-i)*(x-4+i) where each factor is x minus a root. Then multiply these out. = (x-2)*(x2 - 8x + 17) = x3 - 2x2 - 8x2 + 16x + 17x - 34 = x3 - 10x2 + 33x - 34
The answer to the question, as stated, is that the other root could be anything. However, if all the coefficients of the quadratic equation are real numbers, then the other root is 1 minus 3i.
There are no factors with rational coefficients.
The are under the curve on the domain (a,b) is equal to the integral of the function at b minus the integral of the function at a
1.25 cubic feet - 77 cubic feet = -75.75 cubic feet.
Translate to what? I assume you need help interpreting it. The quadratic equation is used to solve the quadratic polynomial, ax2 + bx + c = 0, where a, b, and c can be any number. For example, if you need to solve the equation x2 = 5 + 2x, you first convert it into the standard form mentioned above: x2 - 2x - 5 = 0. Now find the coefficients, a, b, and c. In this case, a = 1, b = -2, c = -5. Finally, you replace these coefficients in the quadratic equation. The "plus-minus" sign simply means that the quadratic equation is a shortcut for two equations - one in which you add, the other in which you subtract, the terms at the top. The solutions given by the quadratic equation are values of "x" that satisfy the equation.
the integral of the square-root of (x-1)2 = x2/2 - x + C
Look at the coefficients. -16 - 14 = -30. Therefore, -16n - 14n = -30n.
The required equation is: -7x = 63
2bc + 8b - 3c - 12 is an expression, not an equation or inequality. It cannot, therefore have "an answer".
With the help of the quadratic equation formula
The quadric equation is: negative b plus or minus the square root of b squared minus 4ac all over(divided by) 2a