# 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.

Direction: Solve each problem carefully and show your solution in each item.

#### Number of problems found: 27

- Multiplied 78494

A quarter of an unknown number multiplied by 4 equals 30% of that unknown number. Determine the unknown number. - 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? - Right triangle generator

Detective Harry Thomson found on the Internet a generator of the lengths of the sides of right triangles according to which he must apply: a = 2xy, b = x² - y², c = x² + y², where are natural numbers and x & gt; y. Is it a working generator? - 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 an even index) has a value of 42. Find these members. - Given 2

Given g(x)=x²+x+1 where x=t². What is g(t²)? - Polynomial roots

Find the other zeroes of the polynomial 2x^{4}+3x³-3x²-6x-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 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. - 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 is a right triangle. Its hypotenuse is 30 meters long, and its circumference is 72 meters. What are the sizes 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), 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 the circle if AB is 4 cm from the circle's center and BC 8 cm from the center. - 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. - 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 the following equation with quadratic members and rational function: (x²+1)/(x-4) + (x²-1)/(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] - Rotating 7947

In the rotating cone = 100π S rotating cone = 90π v =? r =? - Diamond diagonals

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

Solve a goniometric equation: sin^{4}θ - 1/cos² θ=cos² θ - 2

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