For what value(s) of b will x^2 + bx + 3 have exactly one root?
I'm rather new at this but wouldn't b=2*sqrt(3) give (x+sqrt3)2 as factors and that would give one root?
Check my thinking.
for a quadratic equation to have exactly one root, the discriminat must be zero i.e
if equation is:
ax^2+bx+c=0 , then for exactly one root,
b^2-4ac=0
i.e.
b^2=4ac
for your equation,
x^2+bx+3=0
b^2=4(1)(3)
=12
hence
b=sqrt(12)
=2(sqrt(3))
You are correct in your thinking. To find the value of b that will give the quadratic equation x^2 + bx + 3 exactly one root, we can use the fact that the discriminant, b^2 - 4ac, must be equal to zero.
In this case, the quadratic equation is x^2 + bx + 3 = 0, where a = 1, b = b, and c = 3.
So we have:
b^2 - 4(1)(3) = 0
Simplifying further:
b^2 - 12 = 0
To solve for b, we can add 12 to both sides:
b^2 = 12
And then take the square root of both sides:
b = ±√12
Since we're looking for a value of b that will give exactly one root, we take the positive square root:
b = √12 = 2√3
So the value of b that will give x^2 + bx + 3 exactly one root is b = 2√3.