Question

Find the roots of the following equations by the method of

completing the square.

5x2+3x+6=0​

Answer 1

Answer:

Step-by-step explanation:

$5x { }^{2} + 3x + 6 = 0 \\ (x + \frac{3}{2} ) {}^{2} - \frac{9}{4} + \frac{24}{4} \\ (x + \frac{3}{2} ) {}^{2} + \frac{15}{4} \\ (x + \frac{3}{2} ) {}^{2} + ( \frac{ \sqrt{15} }{2} ) {}^{2} \\ (x + \frac{3}{2} - \frac{ \sqrt{15} }{2} )(x + \frac{3}{2} + \frac{ \sqrt{15} }{2} ) \\ (x + 3 - \sqrt{15} )( x + 3 + \sqrt{15} ) \\ x = - 3 - \sqrt{15} \: (or) - 3 + \sqrt{15}$