compute the discriminant of the equation.What does the discriminant indicate about the kinds of solution?
7xsquared=2x-5
Perhaps if you show some effort in trying to solve these problems, a tutor may be able to help you.
I suppose by "disciminant" you mean the term b^2 - 4ac. To find out what a, b and c are, rewrite the equati9n in the form
ax^2 + bx + c = 0
That means a=7, b=-2 and c=5. That makes discriminant a large negative number. The two roots are imaginary.
To compute the discriminant of a quadratic equation, you first need to express the equation in standard form, which is in the form of ax^2 + bx + c = 0. In this case, the given equation is 7x^2 = 2x - 5.
To convert this equation to standard form, subtract 2x from both sides and add 5 to both sides:
7x^2 - 2x + 5 = 0
Now, you can identify the values of a, b, and c from the equation. In this case, a = 7, b = -2, and c = 5.
The discriminant of a quadratic equation is calculated using the formula: Δ = b^2 - 4ac.
So, for the given equation, the discriminant can be calculated as:
Δ = (-2)^2 - 4 * 7 * 5
= 4 - 140
= -136
The discriminant Δ in this case is -136.
Now, let's analyze the significance of the discriminant:
1. If Δ > 0, then the equation has two distinct real solutions.
2. If Δ = 0, then the equation has one real solution (where the parabola touches the x-axis at a single point).
3. If Δ < 0, then the equation has two complex conjugate solutions (no real solutions).
In this case, since Δ = -136, which is less than 0, the equation 7x^2 = 2x - 5 has two complex conjugate solutions, indicating that there are no real solutions.