Embibe Experts Solutions for Exercise 6: Assignment

If $a$ and $b$ are rational and $\alpha , \beta$ be the roots of $x^2+2ax+b=0,$ then the equation with rational coefficients one of whose roots is $\alpha +\beta +\sqrt{{\alpha }^2+{\beta }^2}$ is

Let $\alpha , \beta$ be the roots of $a{x}^2+bx+c=0, \gamma , \delta$ be the roots of $p{x}^2+qx+r=0$ and $D_1$ and $D_2$ be their respective discriminant. If $\alpha , \beta , \gamma , \delta$ are in A.P., then the ratio $D_1:D_2$ is equal to

The value of $k$ if

If the difference of the roots of the equation $x^2+ax+b=0$ is equal to the difference of the roots of the equation $x^2+bx+a=0,$ then

If the equations $p{x}^2+2qx+r=0$ and $p{x}^2+2rx+q=0(q\ne r)$ have a common root, then $p+4 q+4r$ equals

Consider that $f\left(x\right)=a{x}^2+bx+c, D=b^2-4ac,$ then which of the following is not true ?

If $p, q, r$ are real numbers satisfying the condition $p+q+r=0,$ then the roots of the quadratic equation $3p{x}^2+5qx+7r=0$ are

If $ax+\frac{b}{x}\ge c$, $\forall x>0$ and $a, b, c$ are positive constants then