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].
[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].
