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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,
for your equation,

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