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].
[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].
