Q: The discriminant of the quadratic equation $2x^2 - 4x + 3 = 0$ is:

Here $a = 2, b = -4, c = 3$.\nDiscriminant $D = b^2 - 4ac = (-4)^2 - 4(2)(3) = 16 - 24 = -8$.

Question 1

Which of the following is a quadratic equation?

Accepted Answer

Expanding option B: $(x + 1)^2 = 2(x - 3) \Rightarrow x^2 + 2x + 1 = 2x - 6 \Rightarrow x^2 + 7 = 0$, which is of the form $ax^2 + bx + c = 0$ with $a 
eq 0$. Hence, it is a quadratic equation.

Question 2

The degree of a quadratic equation is always:

Accepted Answer

By definition, a polynomial equation of degree 2 is called a quadratic equation. Therefore, the degree of a quadratic equation is 2.

Question 3

For the quadratic equation $ax^2 + bx + c = 0$, the discriminant $D$ is given by:

Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is defined as $D = b^2 - 4ac$.

Question 4

If the discriminant $D = 0$, then the roots of the quadratic equation are:

Accepted Answer

When the discriminant $D = b^2 - 4ac = 0$, the quadratic equation has two real and equal (coincident) roots.

Question 5

The discriminant of the quadratic equation $2x^2 - 4x + 3 = 0$ is:

Accepted Answer

Here $a = 2, b = -4, c = 3$.
Discriminant $D = b^2 - 4ac = (-4)^2 - 4(2)(3) = 16 - 24 = -8$.

Quadratic Equations