Question

write the discriminant of the quadratic equation 4x2 -px+12=0​

Answer 1

The given quadratic equation:

4$x^2$ - px + 12 = 0​

Here, a = 4, b = - p and c = 12

We have to find, the discriminant of the given quadratic equation.

Solution:

We know that:

∴ Discriminant(D) = $b^{2}$ - 4ac

                              = $(-p)^{2}$ - 4(4)(12)

                               = $p^{2}$ - 16(12)

                              = $p^{2}$ - 192

∴ Discriminant(D) =  $p^{2}$ - 192

Thus, the discriminant of the given quadratic equation is "$p^{2}$ - 192".

Answer 2

Given:

The quadratic equation: 4x² - px + 12 = 0​

To find:

Write the discriminant of the quadratic equation.

Solution:

From given, we have the data as follows.

The quadratic equation: 4x² - px + 12 = 0​

The discriminant is given by the formula,

D = b² - 4ac

From given, we have,

a = 4, b = - p and c = 12

Substitute the values in the above equation.

D = (- p)² - 4 × 4 × 12

D = p² - 192

Therefore, the discriminant of the quadratic equation 4x² - px + 12 = 0​ is (p² - 192)