Quadratic equation + square (second power, quadratic) - practice problems - last page

Number of problems found: 292

Biquadratic
By introducing a new variable, solve the biquadratic equation: - x ⁴ +277 x² -15876=0
Quadratic equation
Determine the numbers b and c that the numbers x₁ = -7 and x₂ = 5 were roots of the quadratic equation: -3x ² + b x + c = 0
Special cube
Calculate the cube's edge if its surface and volume are numerically equal numbers.
Rectangle SS
The perimeter of a rectangle is 154 dm, and its diagonal is 62.36 dm. Find the dimensions of the rectangle.

Heron backlaw
Calculate the unknown side in a triangle with sides 24 and 40 and area 299.6.
Quadratic equation
Quadratic equation 7x²+bx+c=0 has roots x₁ = 67 and x₂ = -84. Calculate the coefficients b and c.
Right triangle
The legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
Golden ratio
Divide the line of length 871 cm into two sections so that the ratio of shorter to greater is the same as the ratio of the greater section to the whole length of the line.
Tangents
To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle center.

Quadratic equation
Solve a quadratic equation: 2x²+28x-550=0
Bomber
Bomber flies 10 km at 600 km/h. At what horizontal distance from the target must the pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s².
Trolleybus
Trolleybus line No. 215 measured 30 km. If the trolley bus goes faster by 4 km/h, the way there and back would be shorter by 39 minutes. Calculate the trolley bus speed and time for a return trip.

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