Question

Find the discriminant and state the nature of the roots. 2x² + 4x + 2 = 0

Answer 1

The discriminant of the quadratic equation 2x² + 4x + 2 is zero, indicating that there is exactly one real and repeated root.

Step-by-step explanation:

To find the discriminant of a quadratic equation of the form ax² + bx + c = 0, you would use the formula b² - 4ac. Applying this to the equation 2x² + 4x + 2 = 0, we have a = 2, b = 4, and c = 2. Thus, the discriminant will be (4)² - 4(2)(2), which simplifies to 16 - 16 and equals 0.

The discriminant being zero implies that the equation has a single real root, or in other words, it has one real solution because both roots are identical. Therefore, the nature of the roots is that they are real and equal.

Answer 2

d=b^2-4ac

=4^2-4*2*2

=16-16

=0

nature-roots are equal.