Question

By using the method of completing the square, show that the equation 4x²+3x+5=0 has no real roots.

Answer 1

Step-by-step explanation:

Here is your answer dude

Answer 2

SOLUTION

Given,

4x² +3x+5=0

$= > {x}^{2} + \frac{3}{4} x + \frac{5}{4} x = 0 \\ \\ = > {x}^{2} + 2( \frac{3}{8} x) = - \frac{5}{4} \\ \\ = > {x}^{2} + 2( \frac{3}{8} x) + ( \frac{3}{8} ) {}^{2} = (\frac{3}{8} ) {}^{2} - \frac{5}{4} \\ \\ = > (x + \frac{3}{8} ) {}^{2} = - \frac{71}{64}$

Since, R.H.S. is negative. Here

$(x + \frac{3}{8} ) {}^{2}$

can't be negative for any real value of x. So, the given condition has no real roots.

Hope it helps ☺️