Question

For what values of p are the roots of the equation `4x^2+px+3=0` real and equal? 

Answer 1

The given equation is `4x^2+px+3=0` 

This is of the form `ax^+bx+c=0` where `a=4, b=p and c=3` 

∴` D=b^2-4ac=p^2-4xx4xx3=p^2-48` 

The given equation will have real and equal roots if D = 0.  

∴ `p^2-48=0` 

⇒`p^2=48` 

⇒`p=+-sqrt48=+-4sqrt3` 

Hence, `4sqrt3` and `-4sqrt3` are the required values of p.