# 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

- Biquadratic

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 2x^{4}+3x³-3x²-6x-2, if two of them are root2 & -root2 - Given 2

Given g(x)=x^{2}+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] - 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. - Substitution method

Solve a goniometric equation: sin^{4}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 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.

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