Nature of Roots Using Discriminant

Q. If the equation $x^2+4x-k=0$ has real and distinct roots, then :

1. $k<-4$
2. $k>-4$
3. $k\le -4$
4. $k\ge -4$

Q. For what value of $m$ does the equation, $x^2+2x+m=0$ have two distinct real roots?

1. m = 1
2. m < 1
3. m >1
4. m > 2

Q. Find the value of k for which the roots of the equation $k{x}^2+4x+1=0$ are real and equal.

1. 0
2. 3
3. 4
4. 2

Q.

If the equation $9x^2+6kx+4=0$ has real and equal roots, then find the value of k.

1. zero

2. either 2 or zero

3. either –2 or zero

4. either 2 or –2

Q.

Find the values of k for which the given equation has real and equal roots: [3 MARKS]

$x^2-2x(1+3k)+7(3+2k)=0$

Q.

Without solving, examine the nature of roots of the equations 2$x^2$ – 5x + 5 = 0

Q. Question 1 (i)
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;
(i) $2x^2-3x+5=0$

Q. Find the values of k for which the given equation has real and equal roots:

$x^2-2x(1+3k)+7(3+2k)=0$

Q. Question 1 (iii)
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;
$\left(iii\right)2x^2-6x+3=0$

Q. The roots of the equation $2x^2+4x+5$ = 0 are .

1. real & equal
2. real & unequal
3. not real

Q. The roots of the equation $2x^2+4x+5$ = 0 are .

1. real & unequal
2. not real
3. real & equal

Q. Find the values of k for which the given equation has real and equal roots:

$x^2-2x(1+3k)+7(3+2k)=0$

Q. Find the value of $k$ for which the equation $x^2+k(2x+k-1)+2=0$ has real and equal roots.

Q. For what integer value/s, of k, the quadratic equation $(1-k)x^2-4kx+2=0$ has real and equal roots?

1. $-1$
2. $\frac{1}{2},-1$
3. $\frac{1}{2}$
4. None of these

Q. Find the values of k for which the given equation has real and equal roots:

$x^2-2x(1+3k)+7(3+2k)=0$

Q.

The equation (m being real), $m{x}^2+2x+m=0$ has two distinct roots if ___.

1. m $\ne$ 0, 1

2. m $\ne$ 1, – 1

3. m $\ne$ 0, 1, –1

4. m$\ne$0

Q. The roots of the equation $2x^2+4x+5$ = 0 are .

1. real & equal
2. real & unequal
3. not real

Q.

Find the values of k for which the given equation has real and equal roots: [3 MARKS]

$x^2-2x(1+3k)+7(3+2k)=0$

Q.

If the equation $9x^2+6kx+4=0$ has equal roots, then find the value of k =

1. -2, 0

2. 0

3. $\pm 2$

4. 2 , 0

Q.

If the equation $x^2+2(k+2)x+9k=0$ has equal roots, then values of k are __________.

1. 1 or 4

2. –1 or 5

3. –1 or –4

4. 1 or –5

Q.

If the roots of equation $x^2+4x+c=0$ are real then $c\ge 4$.

1. False

2. True

Q. The equation $k^2{x}^2+kx+1=0$ has ____

1. one real root
2. two real roots
3. no real roots
4. equal roots

Q. What is the condition for the equation $x^2+bx-c=0$ to have real roots?

1. $b^2+4ac\ge 0$
2. $b^2-4ac>0$
3. $b^2\ge -4c$
4. $b^2\ge 4c$