Tag: maths

The roots of equation $\displaystyle x^{2}+px+q=0$ are $1 $ and $2$ . The roots of the equation $\displaystyle qx^{2}-px+1=0$ must be

The equation whose roots are twice the roots of $x^2 -3x +3=0$ is

The equation whose roots are the squares of the roots of equation $x^2 -x +1= 0$ is

If $m$ and $n$ are the roots of the equation $(x + p)(x + q) - k = 0$, then the roots of the equation $(x - m)(x - n) + k = 0$ are-

If $\alpha$ and $\beta$ are the roots of $x^{2} + p = 0$ where p is a prime, which equation has the roots $\dfrac {1}{\alpha}$ and $\dfrac {1}{\beta}$?

The equation formed by multiplying each root of $ax^2  + bx + c = 0$ by 2 is $ x^2 + 36x + 24 = 0$.Which one of the following is correct ?

If $\alpha , \beta$ are the roots of the equation $ax^2+bx+c=0$ then the quadratic equation whose roots are $\alpha + \beta , \alpha \beta$ is:

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$ and if $px^2+qx+r=0$ has roots $\displaystyle \frac{1-\alpha}{\alpha}$ and $\displaystyle \frac{1-\beta}{\beta}$, then $r$ is

If $\alpha , \beta$ are the roots of the equation $9x^2+6x+1=0$, then the equation with the roots $\cfrac{1}{\alpha}, \cfrac{1}{\beta}$ is :

If $\alpha$ and $\beta$ are roots of $2{ x }^{ 2 }-3x-6=0$, then the equation whose roots are ${ \alpha  }^{ 2 }+2$ and ${ \beta  }^{ 2 }+2$ will be