Algebra Questions from Analizemath
- Order from greatest to least
- Find all rational zeros of P(x) = x3 – 7x + 6.
- Round all real zeros in the graph to the nearest integer and find a polynomial function P of lowest degree, with the absolute value of the leading coefficient equal to 1, that has the indicated graph.
- 2 – i, where i is the imaginary unit, is a zero of P(x) = x4 – 4x3 + 3x2 + 8x – 10. Find all zeros of P.
- Find a, b and c so that the graph of the quadratic function f(x) = ax2 + bx + c has a vertex at (-2 , 1) and passes through the point (0 , -3).
- f(x) is a quadratic function such that f(1) = 3 and f(5) = 3. Find the x coordinate of the vertex of the graph of f.
- Find a and b so that the rational function f(x) = (ax4 + bx3 + 3) / (x3 – 2) has an oblique asymptote given by y = 2x – 3
- Solve for x the equation log9(x3) = log2(8)
- Find the value of logy(x4) if logx(y3) = 2
- Solve for x the equation logx(8e3) = 3
- If 8x + 8x – 1 = 10, find 22x.
- If a2 – b2 = 8 and a*b = 2, find a4 + b4.
- What are the maximum value and minimum values of f(x) = |2sin(2x – pi/3) – 5| + 3
- If x < -7, simplify |4 – |3 + x||
- A car travels from A to B at an average speed of 50 km/hour. At what average speed would it have to travel from B to A to average 60 km/hour for the whole trip?
- If x2 – y2 = -12 and x + y = 6, find x and y.
- f(x) is a function such that f(x) + 3f(8 – x) = x for all real numbers x. Find the value of f(2).
- f(x) is a function such that f(2x + 1) = 2f(x) + 1 for all real numbers x and f(0) = 2. Find the value of f(3).
- Find b so that the line y = 2x + b is tangent to the circle x2 + y2 = 4.
- What is the remainder of the division (x100 – x99 – x + 1) / (x2 – 3x + 2)
- Evaluate the number represented by the infinite series sqrt(1/3 + sqrt(1/3 + sqrt(1/3 + …))).
- Show that the 3 by 3 system of equations given below has no solutions.
2x + y – 3z = 5
-5x + 3y + 2z = 7
3x – 4y + z = 8
This picture is for number three problem