High School

What is the discriminant of the quadratic equation [tex]-4x^2 - 7x - 6 = 0[/tex]?

A. 145
B. -47
C. -145
D. 47

Answer :

We start with the quadratic equation

[tex]$$-4x^2 - 7x - 6 = 0.$$[/tex]

The discriminant of a quadratic equation of the form

[tex]$$ax^2 + bx + c = 0$$[/tex]

is given by

[tex]$$\Delta = b^2 - 4ac.$$[/tex]

For our equation, the coefficients are

[tex]$$a = -4,\quad b = -7,\quad c = -6.$$[/tex]

Step 1: Compute [tex]$b^2$[/tex].

[tex]$$b^2 = (-7)^2 = 49.$$[/tex]

Step 2: Compute [tex]$4ac$[/tex].

[tex]$$4ac = 4 \cdot (-4) \cdot (-6) = 96.$$[/tex]

Step 3: Calculate the discriminant.

[tex]$$\Delta = b^2 - 4ac = 49 - 96 = -47.$$[/tex]

Thus, the discriminant of the quadratic equation is [tex]$\boxed{-47}$[/tex].