Find the discriminant of the quadratic equation state solutions 4a^2+7a+4=0
b^2 - 4ac
= 49 - 4(4)(4) = -15
To find the discriminant of a quadratic equation, we can use the formula:
Discriminant (D) = b^2 - 4ac
In the quadratic equation, ax^2 + bx + c = 0, a, b, and c represent the coefficients.
Let's find the discriminant for the given equation: 4a^2 + 7a + 4 = 0.
In this equation, a = 4, b = 7, and c = 4.
Using the formula for the discriminant:
D = (7)^2 - 4(4)(4)
D = 49 - 64
D = -15
Therefore, the discriminant (D) is -15.
The discriminant can be used to determine the nature of the solutions of the quadratic equation. If the discriminant is positive (D > 0), the equation has two distinct real solutions. If the discriminant is zero (D = 0), the equation has only one real solution (the roots are repeated). If the discriminant is negative (D < 0), the equation has no real solutions (the roots are complex conjugates).
In this case, since the discriminant is -15 (negative), the quadratic equation 4a^2 + 7a + 4 = 0 has no real solutions.