by using the method of completing the square show that the 4x^2+3x+5=0

1.	by using the method of completing the square show that the 4x^2+3x+5=0 has no real roots
Answer» We have,4x2 + 3x + 5 = 0Divide whole equation by 4{tex} \\Rightarrow \\quad x ^ { 2 } + \\frac { 3 } { 4 } x + \\frac { 5 } { 4 } = 0{/tex}{tex}\\Rightarrow \\quad x ^ { 2 } + 2 \\left( \\frac { 3 } { 8 } x \\right) = - \\frac { 5 } { 4 }{/tex}Add ( half of coefficient of x )2 both sides{tex}\\Rightarrow \\quad x ^ { 2 } + 2 \\left( \\frac { 3 } { 8 } \\right) x + \\left( \\frac { 3 } { 8 } \\right) ^ { 2 } = \\left( \\frac { 3 } { 8 } \\right) ^ { 2 } - \\frac { 5 } { 4 }{/tex}{tex}\\Rightarrow \\quad \\left( x + \\frac { 3 } { 8 } \\right) ^ { 2 } = - \\frac { 71 } { 64 }{/tex}{tex}\\left( x + \\frac { 3 } { 8 } \\right) ^ { 2 }{/tex} cannot be negative for any real value of x. Hence, the given equation has no real roots.

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