Use the discriminate to determine how many real number solutions the equation has.
s^2 - 5s + 6 = 0
the discriminant= b2-4ac
a=1 b=-5 c=6
25-4(1)(6)=1
Since 1 > 0, the polynomial has two real roots, if the discriminant = 0, the polynomial has one real root, and if it's < 0, the polynomial has no real roots
I still don't understand. Could you explain. I don't know what any of this means.
When you have an equation, s^2-5s+6=0, you can find the discriminant by b^2-4ac. The co-efficient (what comes before) the squared term is a, in this case 1. The co-efficient before the s is b (-5), and the last term is c (6). 25-4(1)(6)=1. When it is more than 0, the polynomial has two real roots (or answers). If the discriminant is equal to 0, the polynomial has one real root, and if it's less than 0, the polynomial has no real roots. For this problem, since the discriminant equals 1, it has two real roots. I hope this helps. It's hard to explain through the internet. If you still don't understand, try asking your teacher.
To determine the number of real number solutions of the equation s^2 - 5s + 6 = 0, we can use the discriminant. The discriminant is the expression present under the square root (√) sign in the quadratic formula.
The quadratic formula states that given a quadratic equation in the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = [-b ± √(b^2 - 4ac)] / (2a)
In this case, the equation is s^2 - 5s + 6 = 0, which means a = 1, b = -5, and c = 6.
The discriminant (denoted as Δ or b^2 - 4ac) is used to determine the nature of the roots of a quadratic equation.
If the discriminant is positive (Δ > 0), then the quadratic equation has two distinct real solutions.
If the discriminant is zero (Δ = 0), then the quadratic equation has one real solution (repeated or double root).
If the discriminant is negative (Δ < 0), then the quadratic equation has no real solutions (only complex roots).
In this case, we will calculate the discriminant using the values from the given equation.
Δ = b^2 - 4ac
Δ = (-5)^2 - 4(1)(6)
= 25 - 24
= 1
Since the discriminant (Δ) is greater than zero (Δ > 0), the quadratic equation s^2 - 5s + 6 = 0 has two distinct real solutions.