Embibe Experts Solutions for Chapter: Quadratic Equations, Exercise 2: EXERCISE-2

Let $\alpha ,\beta ,\gamma$ be the roots of the equation $x^3+3a{x}^2+3bx+c=0$. If $\alpha ,\beta ,\gamma$ are in H.P. then $\beta$ is equal to -

Number of solution(s) satisfying the equation $3x^2-2x^3={\log }_2\left(x^2+1\right)-{\log }_{2}x$ is

Number of roots of the equation $x^2·e^{2-\left|x\right|}=1$ is

If $\alpha ,\beta$ are the roots of the quadratic equation $\left(p^2+p+1\right)x^2+(p-1)x+p^2=0$ such that unity lies between the roots then the set of values of $P$ is -

Three roots of the equation, $x^4-p{x}^3+q{x}^2-rx+s=0$ are $\tan A,\tan B\&\tan C$ where $A, B, C$ are the angles of a triangle. The fourth root of the biquadratic is -

If $\alpha$ is a root of the equation $2 x(2 x+1)=1$, then the other root is -

If $b^2\ge 4ac$ for the equation $a{x}^4+b{x}^2+c=0$, then all roots of the equation will be real if

Let $\alpha ,\beta$ be the roots of $x^2-ax+b=0$, where $a\&b\in R$. If $\alpha +3\beta =0$, then -