Answer :
To find the discriminant of the quadratic equation
[tex]$$6x^2 + 2x - 9 = 0,$$[/tex]
we start with the standard formula for the discriminant of a quadratic equation
[tex]$$ax^2+bx+c=0,$$[/tex]
which is given by
[tex]$$\Delta = b^2 - 4ac.$$[/tex]
Here, the coefficients are:
[tex]$$a = 6,\quad b = 2,\quad c = -9.$$[/tex]
Now, follow these steps:
1. Calculate [tex]$b^2$[/tex]:
[tex]$$b^2 = (2)^2 = 4.$$[/tex]
2. Calculate [tex]$4ac$[/tex]:
[tex]$$4ac = 4 \cdot 6 \cdot (-9) = -216.$$[/tex]
3. Substitute these values into the discriminant formula:
[tex]$$\Delta = 4 - (-216).$$[/tex]
4. Simplify the expression:
[tex]$$\Delta = 4 + 216 = 220.$$[/tex]
Thus, the discriminant of the quadratic equation is
[tex]$$\boxed{220}.$$[/tex]
[tex]$$6x^2 + 2x - 9 = 0,$$[/tex]
we start with the standard formula for the discriminant of a quadratic equation
[tex]$$ax^2+bx+c=0,$$[/tex]
which is given by
[tex]$$\Delta = b^2 - 4ac.$$[/tex]
Here, the coefficients are:
[tex]$$a = 6,\quad b = 2,\quad c = -9.$$[/tex]
Now, follow these steps:
1. Calculate [tex]$b^2$[/tex]:
[tex]$$b^2 = (2)^2 = 4.$$[/tex]
2. Calculate [tex]$4ac$[/tex]:
[tex]$$4ac = 4 \cdot 6 \cdot (-9) = -216.$$[/tex]
3. Substitute these values into the discriminant formula:
[tex]$$\Delta = 4 - (-216).$$[/tex]
4. Simplify the expression:
[tex]$$\Delta = 4 + 216 = 220.$$[/tex]
Thus, the discriminant of the quadratic equation is
[tex]$$\boxed{220}.$$[/tex]