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].
[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].
