Discriminants Quiz 1

Question 1

If roots of  $${{	ext{x}}^2} + 4{	ext{k + }}{{	ext{k}}^2} = 0$$ are real then what will be value of $${	ext{k}} \in $$?

Accepted Answer

$$\left[ { - 2,2} \right]$$

Answer

$$\left[ {0,2} \right]$$

Answer

$$\left[ { - 2,0} \right]$$

Answer

$$\left( { - 2,2} \right)$$

Question 2

Roots of $${{	ext{x}}^2} + \left( {{	ext{k}} - 1} ight){	ext{x}} - 2{{	ext{p}}^2} = 0$$ are always:

Accepted Answer

Real

Answer

Real and distinct

Answer

Real and equal

Answer

None of these

Question 3

If $${	ext{P}} \in \left\{ {1,2,3,4} ight\},\,\,{	ext{Q}} \in \left\{ {1,2,3,4,5,6} ight\}$$ then how many ordered pairs of $$({	ext{p,q)}}$$ will make roots of $${{	ext{x}}^2} - {	ext{Px + Q  =  0}}$$ real?

Accepted Answer

$$7$$

Answer

$$6$$

Answer

$$8$$

Answer

$$12$$

Question 4

If roots of $${{	ext{x}}^2} + {	ext{kx}} + 9{	ext{k = }}0$$ are not real then which of the following value $${	ext{k}}$$ can take?

Accepted Answer

$$10$$

Answer

$$ - 10$$

Answer

$$37$$

Answer

$$40$$

Question 5

Find nature of roots of $${{	ext{x}}^2}{	ext{ +  Ax }} - \left( {{	ext{A + 2}}} ight){	ext{  =  0}}$$.

Accepted Answer

Real and distinct

Answer

Real and equal

Answer

Imaginary

Answer

Cannot be determined