# Biquadratic equation - practice problems

The fourth-order equation in the form ax^4 + bx^2 + c = 0 is a biquadratic equation. It is solved by substitution t = x^2, 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.#### Number of problems found: 22

- Members

A geometric sequence with six members has the sum of all six members equal to 63; the sum of the even members (that has even index) has a value of 42. Find these members. - Given 2

Given g(x)=x^{2}+x+1 where x=t². What is g(t²)? - Polynomial roots

Find the other zeroes of the polynomial 2x^{4}+3x^{3}-3x^{2}-6x-2, if two of them are root2 & -root2 - Truncated pyramid

The truncated regular quadrilateral pyramid has a volume of 74 cm^{3}, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's content. 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, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members. - 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. - Rotary cylinder

In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height. - Land boundary

The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary? - Faces diagonals

If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - Geometric progressiob

If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms? - 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. - Eq2 2

Solve following equation with quadratic members and rational function: (x^{2}+1)/(x-4) + (x^{2}-1)/(x+3) = 23 - Hyperbola equation

Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm² and side is 13 cm long. - Substitution method

Solve goniometric equation: sin^{4}θ - 1/cos² θ=cos² θ - 2 - MO Z8-I-1 2018

Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David. - Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - Diamond diagonals

Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm. - Cuboid

Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm³. Calculate the length of the other edges.

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