Question

show that √2 and -2√2 are the roots of the equation x^2+√2x-4=0​

Answer 1

Given :

Equqtion : x² + √2x - 4 = 0

To Show :

We have to show that √2 and -2√2 are the roots of the equation.

Solution :

We know that,

D = b² - 4ac

→ D = (√2)² - 4(1)(-4)

→ D = 2 -(-16)

→ D = 2 + 16

→ D = 18

$\rule{150}{2}$

Now,

x = -b ± √D/2a

→ x = -√2 ± √18/2(1)

→ x = -√2 ± 3√2/2

→ x = -√2 - 3√2/2

→ x = -4√2/2

→ x = -2√2

Or

→ x = -√2 + 3√2/2

→ x = 2√2/2

→ x = √2