Quadratic equations and inequalities

2010004503

Level:

Solve the following inequality. \[ (5-2x)(7x+3) \geq 0 \]

\(x\in \left[ -\frac{3}{7}; \frac{5}{2} \right] \)

\(x\in \left[ -\frac{5}{2}; \frac{3}{7} \right] \)

\(x\in \left( -\infty; -\frac{3}{7} \right] \)

\(x\in \left( \frac{5}{2}; \infty \right) \)

2010004504

Level:

The solution set of one of the following quadratic inequalities is the interval \( [ -3;2 ] \). Determine this inequality.

\(x^{2} +x -6 \leq 0\)

\(x^{2} + x -6 \geq 0\)

\(x^{2} - x -6 \leq 0\)

\(x^{2} - x - 6\geq 0\)

\(x^{2} + x + 6\geq 0\)

2010004505

Level:

Find all the values of \(x\) at which the following expression attains negative value. \[ 2 x^{2} - 7x - 4 \]

\(x\in \left (-\frac{1}{2};4 \right )\)

\(x\in \left (-\infty ;-\frac{1}{2} \right )\cup \left (4;\infty \right )\)

\(x\in \left( -4;\frac{1}{2}\right) \)

\(x\in \left (-\infty ;-4\right )\cup \left (\frac{1}{2};\infty \right )\)

\(x\in \left( -4;-\frac{1}{2}\right) \)

2010007303

Level:

The area of the rectangle is \( 735\,\mathrm{cm}^2 \). Its length is by \( 14\,\mathrm{cm} \) longer than its width. Find the perimeter of the rectangle.

\( 112\,\mathrm{cm} \)

\( 56\,\mathrm{cm} \)

\( 252\,\mathrm{cm} \)

\( 92\,\mathrm{cm} \)

2010007305

Level:

One side of a rectangle is \(40\, \%\) longer than the other. The length of the diagonal is \(\sqrt{666}\,\mathrm{cm}\). Find the area of the rectangle.

\(315\, \mathrm{cm}^2\)

\(777\, \mathrm{cm}^2\)

\(140\, \mathrm{cm}^2\)

\(135\, \mathrm{cm}^2\)

2010007901

Level:

The solution set of one of the following inequalities is \( \left( -\infty; -2\right) \cup \left( 5; \infty \right) \). Identify this inequality.

\(x^{2} - 3x -10 > 0\)

\(x^{2} + 3x -10 > 0\)

\(x^{2} - 3x -10 < 0\)

\(x^{2} + 3x -10 < 0\)

2010007902

Level:

For an integer variable \(x\), find the solution set of the following quadratic inequality. \[ 2x^{2} +5x - 12 < 0 \]

\(\{ -3;-2;-1;0;1\}\)

\(\{-4; -3;-2;-1;0;1\}\)

\(\{-4; -3;-2;-1;0;1;2\}\)

\(\{-1;0;1;2;3\}\)

2010007904

Level:

Find out, how many integer solutions the following inequality has. \[ x^{2} + 3x - 1 \leq 0 \]

2010007905

Level:

Find all \(x\) such that the expression \( 2x^2+8\) is negative.

No such \(x\) exists.

\(x\in \mathbb{R}\)

\(x\in (-2;2)\)

\(x\in (-\infty ;-2)\cup (2;+\infty )\)

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.

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

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

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

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

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Quadratic equations and inequalities

2010004503

2010004504

2010004505

2010007303

2010007305

2010007901

2010007902

2010007904

2010007905

9000020406

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