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What is the discriminant of the quadratic equation [tex]5x^2 + 9x + 7 = 0[/tex]?

A. [tex]-59[/tex]
B. [tex]-221[/tex]
C. [tex]221[/tex]
D. [tex]59[/tex]

Answer :

To find the discriminant of the quadratic equation [tex]\(5x^2 + 9x + 7 = 0\)[/tex], we use the discriminant formula for a quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex], which is:

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

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

Now, substitute these values into the formula:

[tex]\[ \Delta = (9)^2 - 4 \cdot (5) \cdot (7) \][/tex]

Calculate each part:

1. [tex]\( (9)^2 = 81 \)[/tex]
2. [tex]\( 4 \cdot 5 \cdot 7 = 140 \)[/tex]

Subtract these values:

[tex]\[ \Delta = 81 - 140 = -59 \][/tex]

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

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