The number of real solutions of the equation ${\log }_{0.5}x=\left|x\right|$ is

Important Questions on Inequalities and Quadratic Equation

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Target Exercises>Q 200

If ${\left({\log }_{5}x\right)}^2+{\log }_{5}x<2,$ then $x$ belongs to the interval

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 12

Let $\alpha$ and $\beta$ be the roots of equation $x^2-6x-2=0$ If $a_n={\alpha }^n-{\beta }^n,$ for $n\ge 1,$ then the value of $\frac{a_{10}-2a_8}{2a_9}$ is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 13

If $a\in R$ and the equation $-3{\left(x-\left[x\right]\right)}^2+2\left(x-\left[x\right]\right)+a^2=0$ (where, $\left[x\right]$ denotes the greatest integer $\le x$) has no integral solution, then all possible values of $a$ lie in the interval

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 14

If the equations $x^2+2x+3=0$ and $a{x}^2+bx+c=0$ $a,b,c\in R,$ have a common root, then $a:b:c$ is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 15

The equation $e^{\sin x}-e^{-\sin x}-4=0$ has

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 16

Let $\alpha ,\beta$ be real and $z$ be a complex number. If $z^2+\alpha z+\beta =0$ has two distinct roots on the line $Re z=1,$ then it is necessary that

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 17

Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots $\left(4,3\right).$ Rahul made a mistake in writing down coefficient of $x$ to get roots $\left(3,2\right).$ The correct roots of equation are

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 18

If $\alpha$ and $\beta$ are the roots of the equation $x^2-x+1=0$, then ${\alpha }^{2009}+{\beta }^{2009}$ is equal to