Embibe Experts Solutions for Chapter: Theory of Equation, Exercise 1: NDA & NA EE 2019 Paper 1 Mathematics

If $\cot \alpha$ and $\cot \beta$ are the roots of the equation $x^2-3x+2=0,$ then what is $\cot (\alpha +\beta )$ equal to?

The roots $\alpha$ and $\beta$ of a quadratic equation, satisfy the relations $\alpha +\beta ={\alpha }^2+{\beta }^2$ and $\alpha \beta ={\alpha }^2{\beta }^2.$ What is the number of such quadratic equations?

How many real roots does the equation $x^2+3\left|x\right|+2=0$ have?

Consider the following statements in respect of the quadratic equation $4\left(x-p\right)\left(x-q\right)-r^2=0,$ where $p, q$ and $r$ are real numbers.

1. The roots are real.

2. The roots are equal, if $p=q$ and $r=0.$

Which of the above statements is/are correct?

Which one of the following is the second degree polynomial function $f\left(x\right)$ where, $f\left(0\right)=5, f\left(-1\right)=10$ and $f\left(1\right)=6?$

If $p$ and $q$ are the roots of the equation $x^2-30x+221=0,$ what is the value of $p^3+q^3?$

The equation $p{x}^2+qx+r=0$ (where $p, q, r,$ all are positive) has distinct real roots $a$ and $b.$ Which one of the following is correct?

If the roots of the equation $x^2+px+q=0$ are $\tan 19°$ and $\tan 26°,$ then which one of the following is correct?