Quadratic Equations Questions

If the roots of the quadratic equation $x^2+px+q=0$ are $\tan 30^{\circ }$ and $\tan 15^{\circ }$, respectively, then the value of $2+q-p$ is:

All the values of $m$ for which both roots of the equation $x^2-2mx+m^2-1=0$ are greater than $-2$ but less than $4$, lie in the interval:

If the difference between the roots of the equation $x^2+ax+1=0$ is less than $\sqrt{5}$, then the set of possible values of $a$ is:

In a triangle $PQR$, $\angle R=\frac{\pi }{2}$. If $\tan \frac{P}{2}$ and $\tan \frac{Q}{2}$ are the roots of $a{x}^2+bx+c=0,a\ne 0$, then:

The value of $a$ for which the sum of the squares of the roots of the equation $x^2-(a-2)x-a-1=0$ assumes the least value is:

If roots of the equation $x^2-bx+c=0$ are two consecutive integers, then $b^2-4c$ equals:

If both the roots of the quadratic equation $x^2-2kx+k^2+k-5=0$ are less than $5$, then $k$ lies in the interval:

If the sum of the roots of the quadratic equation $a{x}^2+bx+c=0$ is equal to the sum of the squares of their reciprocals, then $\frac{a}{b}$, $\frac{c}{a}$ and $\frac{b}{c}$ are in:

The number of real solutions of the equation $x^2-3|x|+2=0$ is:

The value of '$a$ ' for which one root of the quadratic equation $(a^2-5a+3)x^2+(3a-1)x+2=0$ is twice as large as the other, is:

The quadratic equations $x^2-6x+a=0$ and $x^2-cx+6=0$ have one root in common. The other roots of the first and second equations are integers in the ratio $4:3$. Then the common root is:

If the roots of the equation $b{x}^2+cx+a=0$ be imaginary, then for all real values of $x$, the expression $3b^2{x}^2+6bcx+2c^2$ is:

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

If $(1-p)$ is a root of quadratic equation $x^2+px+(1-p)=0,$ then its roots are

If one root of the equation $x^2+px+12=0$ is $4,$ while the equation $x^2+px+q=0$ has equal roots, then the value of 'q' is

Let two numbers have arithmetic mean $9$ and geometric mean $4.$ Then these numbers are the roots of the quadratic equation