Answer:
The values of b are [tex]\mathbf{b=\pm18}[/tex]
Step-by-step explanation:
We need to find the value of b will cause [tex]27x^2+ bx +3 = 0[/tex] to have one real solution.
If it has one real solution, the discriminant is zero.
The formula of discriminant is: [tex]b^2-4ac[/tex]
In our case: [tex]b^2-4ac=0[/tex]
We have a=27, b=b and c=3
Putting values to find b
[tex]b^2-4ac=0\\b^2-4(27)(3)=0\\b^2-324=0\\b^2=324\\Taking \ square root \ on \ both \ sides\\\sqrt{b^2}=\sqrt{324}\\b=\pm18[/tex]
So, the values of b are [tex]\mathbf{b=\pm18}[/tex]
