Question

find the roots of 4x²+3x+5=0 by the method of completing the square.​

Answer 1

Given Equation

4x²+3x+5=0

Dividing by 4

4x^2/4 + 3x/4 + 5/4 = 0

x²+ 3x /4 + 5 /4

we know that

$(a + b) ^{2} = a ^{2} + 2ab + b ^{2}$

here a=x

2ab=3x/4

2b=3/4

b=3/8

adding and subtracting (3/8)^2

x2+ 3x/4 +5 +(3/8)^2 - (3/8)^2=0

(x+3/8)^2 + 5/4 - (3/8)^2=0

(x+3/8)^2=9/64 - 5/4

(x+ 3/8)^2 = 9-80/64

(x+ 3/8)^2 = -71/64

Since square of any number cannot be negative

So, answer does not exist.

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