If $\mathrm{x}\in \mathrm{R},$ and $\mathrm{K}=\frac{\left({\mathrm{x}}^2-\mathrm{x}+1\right)}{\left({\mathrm{x}}^2+\mathrm{x}+1\right)},$ then:

Important Questions on Theory of Equations

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 15

If $\alpha , \beta , \gamma$ are such that $\alpha +\beta +\gamma =2, {\alpha }^2+{\beta }^2+{\gamma }^2=6, {\alpha }^3+{\beta }^3+{\gamma }^3=8,$ then ${\alpha }^4+{\beta }^4+{\gamma }^4$ is

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 16

The real values of a for which the quadratic equation 2x² - (a³ + 8a - 1) x + a² - 4a = 0 possesses roots of opposite signs are given by :

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 17

If $\alpha , \beta$ are the roots of $a{x}^2+bx+c=0$ and $\alpha +h, \beta +h$ are the roots of $p{x}^2+qx+r=0,$ then what is $h$ equal to?

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 20

The value of $a$ for which the equation $x^2-2(a-1)x+(2a+1)=0$ has both roots positive is

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 21

The number of real solutions of the equation $2^{3x^2-7x+4}=1$is:

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 22

The number of real solutions of the equation $2|\mathrm{x}{|}^2-5|\mathrm{x}|+2=0$ is:

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 24

The given equation $\sqrt{x+1}- \sqrt{x-1}= \sqrt{4x-1}$ has

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 32

The integer $\mathrm{k}$ for which the inequality ${\mathrm{x}}^2-2(4\mathrm{k}-1)\mathrm{x}+15{\mathrm{k}}^2-2\mathrm{k}-7>0$ is valid for any $\mathrm{x}$ is: