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Квадратные неравенства

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Квадратные неравенства

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Тест по квадр. неравенствам

Created by

Адиля Имашева
Адиля Имашева
Kazakhstan

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Квадратные неравенства
 

Квадратные неравенстваOnline version

Тест по квадр. неравенствам

by Адиля Имашева
1

Какое решение для неравенства x²-5x+6>0?

2

Если ax²+bx+c>0 при a>0, где параболa открывается вверх, то решение это:

3

Какое решение неверно для неравенства x^2≤0?

4

Неравенство (x-2)(x+3)≥0 решается как?

5

При каких x выполняется неравенство 2x^2-8x+6<0?

6

Если корни уравнения x²+4x+4=0 равны:

7

Неравенство (x-1)(x-4)≤0 дает решение:

8

Какой метод решить квадратное неравенство без дискриминанта?

9

Неравенство x²-2x+2>0 имеет решение:

Объяснение

Корни уравнения x^2-5x+6=0 равны 2 и 3; график имеет две ветви. Неравенство >0 выполняется вне интервалов от корней.

При >0 парабола выше оси, поэтому вне интервалов между корнями.

Единственный корень — x=0, значение квадратичного выражения минимально равное 0.

Знак неравенства сохраняется там, где произведение неотрицательно: на концах и вне промежутка между корнями.

D=64-48=16, корни 1 и 3; но пройдено неверно — пересчет: 2x^2-8x+6=2(x^2-4x+3)=2(x-1)(x-3).<0 между корнями 1 и 3.

Уравнение (x+2)^2=0 имеет двойной корень -2.

Произведение ≤0 на интервале между корнями и на самих корнях.

Если дискриминант неизвестен, анализируем знаки на интервалax между возможными корнями.

Дискриминант D=4-8<0; квадр. выражение всегда положительно при любой x.

 
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