For the quadratic equation 0.25x^2 - 1.5x + c = 0, the discriminant is equal to 4. What is… — ACT

For the quadratic equation $0.25x^2 - 1.5x + c = 0$ , the discriminant is equal to $4$ . What is the value of the constant $c$ ?

The value of the constant

c

-1.75

The correct option is

-1.75

. To find the value of

c

, substitute the coefficients

a = 0.25

b = -1.5

, and the discriminant

D = 4

into the formula

D = b^2 - 4ac

. This gives

4 = (-1.5)^2 - 4(0.25)c

, which simplifies to

4 = 2.25 - c

. Solving for

c

yields

c = 2.25 - 4 = -1.75

Identify the values of the coefficients from the quadratic equation

0.25x^2 - 1.5x + c = 0

The coefficients are

a = 0.25

b = -1.5

, and the constant is

c

These coefficients are required to compute the discriminant.

Recall the formula for the discriminant

D

and substitute the known values, including the given discriminant

D = 4

4 = (-1.5)^2 - 4(0.25)c

This sets up an equation to solve for the unknown constant

c

Simplify the squared term and the multiplication of the coefficients.

4 = 2.25 - 1c

, which simplifies to

4 = 2.25 - c

Squaring

-1.5

yields

2.25

, and

4(0.25) = 1

Solve the linear equation for

c

c = -1.75

Subtracting

2.25

from both sides gives

1.75 = -c

, which means

c = -1.75

Using the discriminant formula

D = b^2 - 4ac

to solve for an unknown coefficient in a quadratic equation.

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