Answer :

To find the discriminant of the quadratic equation [tex]\(-4x^2 - 7x - 6 = 0\)[/tex], we can use the formula for the discriminant, which is given by:

[tex]\[ D = b^2 - 4ac \][/tex]

where [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are the coefficients of the quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex].

For the given quadratic equation:

- [tex]\(a = -4\)[/tex]
- [tex]\(b = -7\)[/tex]
- [tex]\(c = -6\)[/tex]

Now, let's plug these values into the discriminant formula:

[tex]\[ D = (-7)^2 - 4(-4)(-6) \][/tex]

Calculating step-by-step:

1. [tex]\(b^2 = (-7)^2 = 49\)[/tex]
2. [tex]\(4ac = 4 \times (-4) \times (-6) = 96\)[/tex]

Substitute these values back into the discriminant formula:

[tex]\[ D = 49 - 96 \][/tex]

Finally, calculate the result:

[tex]\[ D = -47 \][/tex]

So, the discriminant of the quadratic equation [tex]\(-4x^2 - 7x - 6 = 0\)[/tex] is [tex]\(-47\)[/tex].

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