Can someone help me with this question? Use the discriminant to determine whether the following equations have solutions that are:two different rational solutions: two different irrational solutions: exactly one rational solution: or two different imaginary solutions.
s^2-5s-6=0
the discriminant is b^2 - 4ac
= 25 - 4(1)(-6) = 49
which is a perfect square , so the square root part will come out exact,
so you will have 2 different rational roots.
Certainly, I can help you with that!
To determine the nature of the solutions of the quadratic equation s^2-5s-6=0 using the discriminant, you need to know the formula for the discriminant and how to use it.
The discriminant (denoted as Δ) is given by the formula Δ = b^2 - 4ac, where the quadratic equation is in the form ax^2 + bx + c = 0. In this case, for the equation s^2-5s-6=0, a = 1, b = -5, and c = -6.
Step 1: Substitute the values of a, b, and c into the discriminant formula.
Δ = (-5)^2 - 4(1)(-6)
Step 2: Simplify the expression inside the parentheses and exponentiation.
Δ = 25 - 4(-6)
Step 3: Simplify further by distributing the negative sign.
Δ = 25 + 24
Step 4: Add the values together.
Δ = 49
Now that you have calculated the discriminant (Δ), you can determine the nature of the solutions of the quadratic equation s^2-5s-6=0 based on the value of Δ.
- If Δ is greater than zero (Δ > 0), then the equation has two different rational solutions.
- If Δ is a perfect square and greater than zero (Δ > 0), then the equation has two different irrational solutions.
- If Δ is zero (Δ = 0), then the equation has exactly one rational solution.
- If Δ is negative (Δ < 0), then the equation has two different imaginary solutions.
In this case, Δ = 49, which is greater than zero. Therefore, the equation s^2-5s-6=0 has two different rational solutions.