Embibe Experts Solutions for Exercise 2: EXERCISE 5.2

Let $F\left(x\right)=x^2+4x+1$. Then

If $x\in R$ then $\frac{x^2+2x+a}{x^2+4x+3a}$ can take all real values if;

If the real roots $\alpha$ and $\beta$ of the equation $a{x}^2+bx+c=0$ are real and of opposite sign then the roots of the equation $\alpha (x-\beta {)}^2+\beta (x-\alpha {)}^2$ is/are

If $1$ lies between the roots of the equation $3x^2-3\sin \alpha x-2{\cos }^2\alpha =0$ then $\alpha$ lies in the interval

The value of $\lambda$ for which the equation $2x^2-2(2\lambda +1)x+\lambda (\lambda +1)=0$ may have one root less than $\lambda$ and other root greater than $\lambda$ are given by

If $(4a+c{)}^2<4b^2$ then one root of $a{x}^2+bx+c=0$ lies in

The value of a for which the equation $\left(1-a^2\right)x^2+2ax-1=0$ has roots belonging to $(0, 1)$ is

If $a$ and $b(\ne 0)$ are the roots of the equation $x^2+ax+b=0,$ then find the least value of $x^2+ax+b(x\in R).$