Determine the value of c for which the following quadratic equations
will have one root.
x^2-5x+c=0
I have no idea what formula to use to figure this out.
look at the serd
b^2=4ac
25=4c
c= 25/4
when b^2>4ac, two roots, real
when b^2<4ac, two roots, complex
when b^2=4ac, one real root.
Bob
Well that was simple.
I couldn't find an example in my text like this. Thanks so much.
To determine the value of c for which the quadratic equation has one root, we need to use the discriminant of the quadratic equation.
The discriminant is calculated using the formula b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In the given quadratic equation x^2 - 5x + c = 0, we have a = 1, b = -5, and c as the unknown value.
For the quadratic equation to have one root, the discriminant must be equal to zero (0), since the discriminant determines the nature of the roots.
Setting the discriminant to zero:
0 = b^2 - 4ac
0 = (-5)^2 - 4(1)(c)
0 = 25 - 4c
Now, solve the equation for c:
25 - 4c = 0
4c = 25
c = 25/4
Therefore, the value of c for which the given quadratic equation has one root is c = 25/4.