Nishit K Sinha Solutions for Chapter: X+2 Maths, Exercise 2: Practice Exercises

If the roots of equation$(\mathrm{q}-\mathrm{r}){\mathrm{x}}^2+(\mathrm{r}-\mathrm{p})\mathrm{x}+\mathrm{p}-\mathrm{q}=0$ are equal, then$\mathrm{p}$,$\mathrm{q}$,$\mathrm{r}$ are in:

If $\mathrm{a}(\mathrm{b}-\mathrm{c}){\mathrm{x}}^2+\mathrm{b}(\mathrm{c}-\mathrm{a})\mathrm{xy}+\mathrm{c}(\mathrm{a}-\mathrm{b}){\mathrm{y}}^2$ is a perfect square, then, $\mathrm{a}$, $\mathrm{b}$, $\mathrm{c}$ are in:

The condition that both the roots of quadratic equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$are positive is

The condition that both the roots of the equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ are zero is:

There is a quadratic equation of the form ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ along with $3$conditions.

I. If only the value of $\mathrm{a}$ is correct in the equation, the roots are $\frac{1}{3}$ and 1 .

II. If only the value of $\mathrm{b}$is correct, the roots are $6$and $5$.

III. If only the value of $\mathrm{c}$ is correct, the roots are $-3$ and $-2$.

What is the equation of a quadratic equation opposite in sign to the roots of the given quadratic equation?

Quadratic equations $(2\mathrm{p}-1){\mathrm{z}}^2+(2\mathrm{p}+1)\mathrm{z}+\mathrm{c}=0$ and $(\mathrm{q}+1){\mathrm{y}}^2+(4\mathrm{q}+1)\mathrm{y}+3\mathrm{c}=0$ have the same pair of roots. Given that $\mathrm{c}\ne 0$, what is the value of $(\mathrm{p}+\mathrm{q})$?

Directions : The question below is followed by two statements A and B. Indicate your responses based on the following directives:

Consider integers $\mathrm{x}, \mathrm{y}$ and $\mathrm{z}$. What is the minimum possible value of ${\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2?$

$\mathrm{A}: \mathrm{x}+\mathrm{y}+\mathrm{z}=89$

$\mathrm{B}$ : Among $\mathrm{x}, \mathrm{y}, \mathrm{z}$ two are equal