Maharashtra Board Solutions for Chapter: Quadratic Equations, Exercise 5: Practice Set

If $\alpha , \beta$ are roots of quadratic equation of $2x^2-4x-3=0$ then find the value of $\alpha +\beta$ and $\alpha \beta$
 

Determine the nature of roots of the following quadratic equation.

$m^2+2m+9=0$

Form the quadratic equation from the roots $2-\sqrt{5} \mathrm{and} 2+\sqrt{5}$.

Sum of the roots of a quadratic equation is double their product. Find $k$ if equation is $x^2-4kx+k+3=0$.

$\alpha , \beta$ are roots of $y^2-2y-7=0$. Find ${\alpha }^2+{\beta }^2$.
 

If $\alpha , \beta$ are the roots of $y^2-2y-7=0$. Find ${\alpha }^3+{\beta }^3$.

The roots of the quadratic equation, $3y^2+ky+12=0$ are real and equal. Find $k$.
 

The roots of the quadratic equation, $kx(x-2)+6=0$ are real and equal. Find $k$.