Saket Sharma Solutions for Exercise 1: Exercise 1

If the sum as well as the product of the roots of the equation ${\mathrm{px}}^2-6\mathrm{x}+\mathrm{q}=0$ is $6$ , then what is $(\mathrm{p}+\mathrm{q})$ equal to?

If $\alpha$ and $\beta$ are the roots of the equation $x^2 – 6x + 6 = 0$, what is ${\alpha }^3+ {\beta }^3 + {\alpha }^2 + {\beta }^2 + \alpha + \beta$ equal to?

It is given that the equations $x^2-y^2 = 0$ and $(x —a{)}^2+y^2 =1$ have single positive solution. For this, the value of ‘$a$’ is

What is the point on the xy-plane satisfying $5x+2y=7xy \text{and} 10x+3y=8xy$?

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2+\alpha x+\beta =0$, where $\beta \ne 0$, then what is the value of $\alpha -\beta$?

If the sum of the roots of the equation ${\mathrm{x}}^2-{\mathrm{k}}^2\mathrm{x}+30\mathrm{kx}-161\mathrm{x}-64=0$ is zero, then what is the difference of the roots?

The solution of the equations $\frac{3x-y+1}{3}=\frac{2x+y+2}{5}=\frac{3x+2y+1}{6}$ is given by which one of the following?

$4{\mathrm{x}}^3+12{\mathrm{x}}^2-\mathrm{x}-3$ is divisible by______.