if a quadratic equation with real coefficients has a discrimiant of 225, then what type of roots doe it have? imaginary, rational or irrational?
rational 56= π
To determine the type of roots of a quadratic equation with a discriminant of 225, we first need to understand the discriminant itself. The discriminant is the part of the quadratic formula that appears under the square root sign (√).
For a quadratic equation of the form ax^2 + bx + c = 0, the discriminant is given by the formula Δ = b^2 - 4ac.
In this case, since the discriminant is 225, we can write the equation as Δ = 225.
Now, let's determine the type of roots based on the value of the discriminant:
1. If the discriminant (Δ) is greater than zero, then the equation has two distinct real roots.
2. If the discriminant (Δ) is equal to zero, then the equation has two identical real roots.
3. If the discriminant (Δ) is less than zero, then the equation has two complex conjugate roots (imaginary roots).
In our case, the discriminant is 225, which is greater than zero. Therefore, the quadratic equation with a discriminant of 225 has two distinct real roots.
To summarize, a quadratic equation with a discriminant of 225 will have two real roots.