Quadratic equations and inequalities

. Decide which of the following equations has the different set of roots than the given equation has, i.e. choose the equation which is not equivalent to the given equation.

2 x + 10 = 8 + 2 x

10 x = 8 x

2 x^{2} + 2 x = 2 x^{2}

x^{2} + 5 x = 4 x + x^{2}

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Choose the equation which has no real roots.

x^{2} + \sqrt{2} = 0

x^{2} + \sqrt{2} x = 0

x^{2} - \sqrt{2} = 0

x^{2} - \sqrt{2} x = 0

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Level:

Choose the equation which has at least one root in

(0; 1]

4 x^{2} - 3 x = 0

3 x^{2} - 4 x = 0

4 x^{2} + 3 x = 0

3 x^{2} + 4 x = 0

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Level:

Choose the equation which has at least one root in

(2; 3)

2 x^{2} - 9 = 0

2 x^{2} + 9 = 0

3 x^{2} - 9 = 0

x^{2} - 9 = 0

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Level:

Choose the equation which has no real roots.

4 x^{2} + 16 = 0

- 4 x^{2} + 16 = 0

16 x^{2} - 4 = 0

\sqrt{2} x^{2} - 2 = 0

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Level:

Choose the equation which has the double root equal to zero.

2 x^{2} = 0

x^{2} + x = 0

x^{2} - x = 0

- x^{2} + x = 0

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Level:

Choose the interval in which all the roots of the following equation lie.

5 x^{2} - 7 x = 0

[- \frac{7}{5}; \frac{7}{5}]

[- 1; 1]

(0; 2]

[- \frac{7}{5}; 0]

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Level:

Choose the interval in which at least one root of the following equation lies.

x^{2} - 8 = 0

[2; 3]

[3; 4]

[- 1; 1]

[- 8; - 5]

Quadratic equations and inequalities

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