Answer :

Sure! To find the discriminant of the quadratic equation [tex]\(5x^2 + 9x + 7 = 0\)[/tex], we use the formula for the discriminant, which is given by:

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

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

In this equation, the coefficients are:
- [tex]\(a = 5\)[/tex]
- [tex]\(b = 9\)[/tex]
- [tex]\(c = 7\)[/tex]

Now, let's substitute these values into the formula:

1. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
b^2 = 9^2 = 81
\][/tex]

2. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4ac = 4 \times 5 \times 7 = 140
\][/tex]

3. Subtract [tex]\(4ac\)[/tex] from [tex]\(b^2\)[/tex] to find the discriminant:
[tex]\[
D = 81 - 140 = -59
\][/tex]

Therefore, the discriminant of the quadratic equation [tex]\(5x^2 + 9x + 7 = 0\)[/tex] is [tex]\(-59\)[/tex].

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