Quadratic Equations Problems - page 9 of 28
Number of problems found: 545
- Roots and coefficient
In the equation 2x² + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b. - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - Intersections 3
Find the intersections of the circles x² + y² + 6 x - 10 y + 9 = 0 and x² + y² + 18 x + 4 y + 21 = 0 - On a line
On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1]. - Algebra
If x+y=5, find xy (find the product of x and y if x+y = 5) - Trapezium
The lengths of parallel sides of a trapezium are (2x+3) and (x+8), and the distance between them is (x+4). If the area of the trapezium is 590, find the value of x. - Rectangle vs square
One side of the rectangle is 1 cm shorter than the side of the square. The second side is 3 cm longer than the side of the square. The square and rectangle have the same area. Calculate the length of the sides of a square and a rectangle. - RTriangle 17
The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm, you will reduce the hypotenuse by 4 cm. Determine the length of these legs. - Euclid1
The right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c? - Pumps
The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than the second one. How many minutes is filled with the first pump? - Rectangle
The area of a rectangle is 546. Its length is 25 larger than the width. What are the dimensions of the rectangle? - Party
At the party, everyone clinked with everyone. Together, they clink $strng times. How many people were at the party? - Calculate 6414
If we add the same number x to the numbers -1,3,15,51, we get the first four members of the geometric sequence. Calculate the number x and the first four members of the geometric sequence. - The area 3
The area of a rectangle is given by the expression 4x² + 5x -6. What is the length of the rectangle if its width is x+2? - A yard
Yevgen is fencing in a yard that is 30 meters longer than it is wide. The yard will have an area of 1000 m². Find its width and length. - Consider
Consider all square prisms with a height of 10 cm. If x is the measurement of the base edge in cm, and y is the prism's volume in cm³. Graph the function - The sum
The sum of the squares of two immediately following natural numbers is 1201. Find these numbers. - Hard cone problem
The cone's surface is 200 cm², and its height is 7 centimeters. Calculate the volume of this cone. - 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. - Cuboid walls
Suppose the areas of three adjacent faces of a cuboid are 8 cm², 18 cm², and 25 cm². Find the volume of the cuboid.
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