3x^2+9x+4=0 the discriminant is 33, using the discriminant to determine the number of real solutions
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http://www.regentsprep.org/Regents/math/algtrig/ATE3/discriminant.htm
To determine the number of real solutions for a quadratic equation using the discriminant, you need to calculate the discriminant and analyze its value. The discriminant is calculated using the formula:
Discriminant (D) = b^2 - 4ac
where a, b, and c are the coefficients of the quadratic equation (ax^2 + bx + c = 0).
In your equation, 3x^2 + 9x + 4 = 0, the coefficients are:
a = 3
b = 9
c = 4
Now, plug these values into the discriminant formula:
D = (9)^2 - 4 * (3) * (4) = 81 - 48 = 33
Therefore, the discriminant is 33.
To determine the number of real solutions, you need to compare the value of the discriminant to zero.
1. If the discriminant is greater than zero (D > 0), then the equation has two distinct real solutions.
2. If the discriminant is equal to zero (D = 0), then the equation has one real solution.
3. If the discriminant is less than zero (D < 0), then the equation has no real solutions.
In this case, the discriminant is 33, which is greater than zero (D > 0). Therefore, the equation has two distinct real solutions.