Nature Of Roots

Q.

Write the discriminant of the equation $3x^2-17x+20=0$ and determine the nature of the roots.

Q.

Write the discriminant of $\sqrt{2}{x}^2-3\sqrt{5}x+\sqrt{18}=0$ and determine the nature of its root.

Q.

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

1. m = 1

2. m < 1

3. m >1

4. m > 2

Q. The number of real roots of the equation $(x-1{)}^2+(x-2{)}^2+(x-3{)}^2=0$ is :

1. $1$
2. $2$
3. $3$
4. None of these

Q. What will be the nature of roots of quadratic equation $2x^2-4x+3=0$ ?

Q.

Choose the correct options: the equation (m being real), $m{x}^2+2x+m=0$ has two distinct roots if -

1. m = 1

2. -1 < m < 1

3. m = -1

4. none of the above

Q. The roots of a quadratic equation $x^2-4x-{\log }_{3}a=0$ are real. Then what is the least value of $a$ ?

1. 64
2. $\frac{1}{64}$
3. $\frac{1}{81}$
4. 81

Q. If $a$ and $b$ are real and $a\ne b$ then show that the roots of the equation $(a-b)x^2+5(a+b)x-2(a-b)=0$ are real and unequal.