By using the method of completing the square, show that the equation `4x^(2)+3x+5=0` has no real roots.

Explanation

We have
`4x^(2)+3x+5=0`
`implies" "4x^(2)+3x=-5`
`implies" "(2x)^(2)+2xx2x xx(3)/(4)+((3)/(4))^(2)=-5+((3)/(4))^(2)`
`" "["adding "((3)/(4))^(2)" on both sides"]`
`implies" "(2x+(3)/(4))^(2)=(-5+(9)/(16))=((-80+9))/(16)=(-71)/(16)lt0.`
But, `(2x+(3)/(4))^(2)` conot be negative for any real value of x.
So, there is no real value of x satisfying the given equation.
Hence, the given equation has no real roots.