What is the value of the discriminant of the quadratic equation 3x^2 + 5x - 2 = 0? — ACT

What is the value of the discriminant of the quadratic equation $3x^2 + 5x - 2 = 0$ ?

Cevap: 49

The discriminant of the quadratic equation is 49.

The discriminant is calculated using the formula

b^2 - 4ac

. For the equation

3x^2 + 5x - 2 = 0

, the coefficients are

a = 3

b = 5

, and

c = -2

. Substituting these yields

5^2 - 4(3)(-2) = 25 - (-24) = 25 + 24 = 49

Identify the coefficients of the quadratic equation

3x^2 + 5x - 2 = 0

in the standard form

ax^2 + bx + c = 0

a = 3

b = 5

, and

c = -2

To use the discriminant formula, we must first extract the constant coefficients corresponding to each term.

Substitute the coefficients into the discriminant formula

D = b^2 - 4ac

D = 5^2 - 4(3)(-2) = 25 - (-24) = 25 + 24 = 49

Calculating the value of the discriminant provides the required solution.

Calculating the discriminant of a quadratic equation to determine the nature of its roots.

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