Biquadratic equation - practice problemsThe fourth-order equation in the form ax4 + bx2 + c = 0 is a biquadratic equation. It is solved by substitution t = x2, which converts the equation into a quadratic equation. It will give us one, two, or no roots. Subsequently, the substitution equation will be solved, which usually doubles the number of roots.
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 27
By introducing a new variable, solve the biquadratic equation: - x 4 +277 x² -15876=0
- Three members GP
The sum of three numbers in GP (geometric progression) is 21, and the sum of their squares is 189. Find the numbers.
- Multiplied 78494
A quarter of an unknown number multiplied by 4 equals 30% of that unknown number. Determine the unknown number.
- Polynomial roots
Find the other zeroes of the polynomial 2x4+3x³-3x²-6x-2, if two of them are root2 & -root2
- Given 2
Given g(x)=x2+x+1 where x=t². What is g(t²)?
- Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
A geometric sequence with six members has the sum of all six members equal to 63; the sum of the even members (that has an even index) has a value of 42. Find these members.
- Substitution method
Solve a goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2
- Geometric progressiob
If the sum of four consecutive terms of a geometric progression is 80 and the arithmetic mean of the second and fourth terms is 30, then find terms.
- Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =?
- Heron backlaw
Calculate the missing side in a triangle with sides 25 and 13 and area 152.
- Combinations 70714
If we increase the number of elements by 1, the number of combinations of the third class without repetitions increases by 10. How many elements do we have?
- Land boundary
The land has a shape of a right triangle. Its hypotenuse has a length of 30m. The circumference of the land is 72 meters. What are the sizes of the remaining sides of the land boundary?
- Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm² and the side is 13 cm long.
- Diamond diagonals
Calculate the diamonds' diagonal lengths if the diamond area is 156 cm square and the side length is 13 cm.
- Rotary cylinder
In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height.
- Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
- The cylinder
In a rotating cylinder, it is given: the surface of the shell (without bases) S = 96 cm² and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder.
- Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's area. Calculate the area of the upper base.
- Sequences AP + GP
The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, the second 4, and keep the third, we get the geometric series. Find AP and GP members.