Amit M Agarwal Solutions for Chapter: Inequalities and Quadratic Equation, Exercise 5: Work Book Exercise 5.5

If $a{x}^2+bx+6=0$ does not have two distinct real roots, then the least value of $3a+b$ is

If $x$ is real, then the least value of the expression $\frac{x^2-6x+5}{x^2+2x+1}$ is

If the quadratic equation $\alpha x^2+\beta x+a^2+b^2+c^2-ab-bc-ca=0$ has imaginary roots, then

Let $S$ denote the set of real values of $a$, for which the roots of the equation $x^2-ax-a^2=0$ exceeds $a$. Then, $S$ equals

$x^4-4x-1=0$ has

The roots $\alpha$ and $\beta$ of the quadratic equation are $a{x}^2+bx+c=0$ are real and of opposite sign. Then, the roots of the equation $\alpha {\left(x-\beta \right)}^2+\beta {\left(x-\alpha \right)}^2=0$ are

If $0<a<5, 0<b<5$ and $\frac{x^2+5}{2}=x-2\cos \left(a+bx\right)$ is satisfied for at least one real $x$, then the greatest value of $a+b$ is

If the roots of $a{x}^2-bx-c=0$ change by the same quantity, then the expression in $a, b$ and $c$ that does not change is