Posted by
**Megan** on
.

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))