Quadratic equations and inequalities

9000020406

Level:

The ratio of the sides of a rectangle is \(3 : 4\). The length of the diagonal is \(100\, \mathrm{cm}\). Find the perimeter of the rectangle.

\(280\, \mathrm{cm}\)

\(150\, \mathrm{cm}\)

\(480\, \mathrm{cm}\)

\(300\, \mathrm{cm}\)

Level:

Solve the following quadratic equation. \[ -x^{2} + 12x - 20 = 0 \]

\(x_{1} = 2\), \(x_{2} = 10\)

\(x_{1} = -2\), \(x_{2} = 10\)

\(x_{1} = -2\), \(x_{2} = -10\)

\(x_{1} = 2\), \(x_{2} = -10\)

Level:

Identify an equation which does not have real solution.

\(x^{2} - 2x + 5 = 0\)

\(x^{2} - 5 = 0\)

\(x^{2} + 0.8x = 0\)

\(- x^{2} + 2x + 35 = 0\)

Level:

Identify an equation which does not have at least one solution in the interval \((0;\infty )\).

\(x^{2} + 5x + 6 = 0\)

\(x^{2} - 2x - 3 = 0\)

\(x^{2} - 10x = 0\)

\(x^{2} - 10x + 24 = 0\)

Level:

Identify an equation which does not have the set \(K = \{ - 3;6\}\) as the set of all solutions of this equation.

\(3x^{2} - 9x + 54 = 0\)

\(2x^{2} - 6x - 36 = 0\)

\(\frac{1} {3}x^{2} - x - 6 = 0\)

\(- x^{2} + 3x + 18 = 0\)