Question

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

Answer 1

SOLUTION :

Given :

$4 {x}^{2} + 3x + 5 = 0$

Now , changing the form of this equation like this ,

${x}^{2} + \frac{3}{4} x + \frac{5}{4} = 0$

${x}^{2} + \frac{3}{4} x = \frac{ - 5}{4}$

${x}^{2} + \frac{3}{4} x + ( { \frac{3}{8} })^{2} = \frac{ - 5}{4} + ({ \frac{3}{8} })^{2}$

$( {x + \frac{3}{8} })^{2} = \frac{ - 5}{4} + \frac{9}{64}$

$( {x + \frac{3}{8} })^{2} = \frac{ - 71}{64} < 0$

There is no real value of x satisfying the given equation. Therefore , the given equation has no real roots.

Note :

While calculating the roots of the equation , divide each side by x coefficient. Rearrange the equation so that the constant term c/a is on the right side (RHS). Add 1/2(b/a) whole square to both sides to make LHS as a perfect square. Write the LHS as a square and simplify the RHS. Solve it.