Question

The
zeroes of the polynomial- 2x2+3√5x+5​

Answer 1

Given equation:-

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

We have to find the possible value of x.

Solution:-

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

$\implies 2 {x}^{2} + 2\sqrt{5} x + \sqrt{5} x + 5 = 0$

$\implies 2x(x + \sqrt{5} ) + \sqrt{5}(x + \sqrt{5}) = 0$

$\implies (2x + \sqrt{5} )(x + \sqrt{5} )= 0$

Therefore, Either 2x+√5=0 or x+√5=0

Therefore,

$x = \frac{ - \sqrt{5} }{2}$

$x = - \sqrt{5}$

Answer:-

$x = \frac{ - \sqrt{5} }{2}$

$x = - \sqrt{5}$