Embibe Experts Solutions for Chapter: Quadratic Equations, Exercise 1: EXERCISE-1

The sum of roots of the equation $a{x}^2+bx+c=0$ is equal to the sum of squares of their reciprocals. Then $b{c}^2,c{a}^2$ and $a{b}^2$ are in -

If the roots of the quadratic equation $x^2+6x+b=0$ are real and distinct and they differ by at most $4$, then the least value of $b$ is

The expression $\frac{x^2+2x+1}{x^2+2x+7}$ lies in the interval; $\left(x\in R\right)-$

The number of integral values of $m$, for which the roots of $x^2-2mx+m^2-1=0$ will lie between $-2$ and $4$ is

If the roots of the equation, $x^3+P{x}^2+Qx-19=0$ are each one more than the roots of the equation, $x^3-A{x}^2+Bx-C=0$, where $A,B,C,P\&Q$ are constants then the value of $A+B+C=$

If $\alpha ,\beta ,\gamma ,\delta$ are roots of $x^4-100x^3+2x^2+4x+10=0$, then $\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }+\frac{1}{\delta }$ is equal to

Number of real solutions of the equation $x^4+8x^2+16=4x^2-12x+9$ is equal to -

Solution set of the inequality, $2-{\log }_2\left(x^2+3x\right)\ge 0$ is