Subject Experts Solutions for Chapter: Quadratic Equations and Inequalities, Exercise 1: PRACTICE EXERCISE

$\alpha ,\beta$ are the roots of the equation $x^2+bx+c=0$ and $S_n={\alpha }^n+{\beta }^n$

Consider the following statements

$\mathrm{I}.$ $S_{n+1}+b{S}_n+c{S}_{n-1}=0$

$\mathrm{II}.$ $S_3=S_1^3-3S_{1}c$

Which of the above statement(s) is / are correct?

In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains $8$ and $2$ for roots. Another student makes a mistake only in the coefficient of first degree term and finds $-9$ and $-1$ for roots. The correct equation is

If $m$ and $n$ are roots of the equation $(x+p)(x+q)-k=0,$ then roots of the equation $(x-m)(x-n)+k=0$ are

If $2p+3q=18$ and $4p^2+4pq-3q^2-36=0$, then what is $(2p+q)$ equal to?

The number of real roots of the equation $x^2-3\left|x\right|+2=0$ is/are

If the sum of the roots of the equation $a{x}^2+bx+c=0$ is equal to the sum of their squares, then

If $x^2-px+4>0$ for all real values of $x$, then which one of the following is correct?

If one root of the equation $(l-m)x^2+lx+1=0$ is double the other and $l$ is real, then what is the greatest value of $m$?