Rational Inequalities Calculator MCQ - Practice Questions & Answers

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Quick Facts

24 Questions around this concept.

Solve by difficulty

If $a + b \sqrt{2} + c \sqrt{3} = 2 - 3 \sqrt{2}$ and $a, b, c \in Q$ , then $a + b + c$ equals

A

3

B

-1

C

2

D

None of these

If $a + b \sqrt{2} = 2 - 3 \sqrt{4}$ and $a, \in b$ Q then $a + b$ equals

A

-1

B

-4

C

3

D

None of these

Concepts Covered - 1

Rational algebraic inequalities

We consider the algebraic inequalities of the following types

$\begin{aligned} \frac{p (x)}{q (x)} < 0, \frac{p (x)}{q (x)} > 0 \\ \frac{p (x)}{q (x)} \leq 0, \frac{p (x)}{q (x)} \geq 0 \end{aligned}$

If p(x) and q(x) can be resolved in factor then we can solve these types of inequalities using a wavy curved method otherwise we use the following method to solve them.

$(1) \begin{aligned} \frac{p (x)}{q (x)} \\ \Rightarrow & > 0 \Rightarrow p (x) q (x) > 0 \\ p (x) & > 0, q (x) > 0 or p (x) < 0, q (x) < 0 \end{aligned}$

(2)

$\begin{aligned} \frac{p (x)}{q (x)} < 0 \Rightarrow p (x) q (x) < 0 \\ \Rightarrow & p (x) > 0, q (x) < 0 or p (x) < 0, q (x) > 0 \end{aligned}$

(3)

$\begin{aligned} \frac{p (x)}{q (x)} \geq 0 \Rightarrow p (x) q (x) \geq 0 and q (x) \neq 0 \\ \Rightarrow p (x) \geq 0, q (x) > 0 or p (x) \leq 0, q (x) < 0 \end{aligned}$

$(4) \begin{aligned} \frac{p (x)}{q (x)} \leq 0 \Rightarrow p (x) q (x) \leq 0 and q (x) \neq 0 \\ \Rightarrow p (x) & \geq 0, q (x) < 0 or p (x) \leq 0, q (x) > 0 \end{aligned}$

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Rational algebraic inequalities

Study other Related Concepts

Rational Inequalities Calculator Current Topic

Algebraic operation on Complex Numbers

Multiplication of Complex Numbers

Conjugates of Complex Numbers

Modulus of complex number and its Properties

Argument of complex number

Polar form of complex numbers

Euler form of complex number

Square root of complex numbers

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