Question

܀
Examine whether the following
quadratic equatians have real
roots. If so, find the roots x2-4x-1=0​

Answer 1

Answer:

$2 + \sqrt{3} \\ 2 - \sqrt{3}$

Step-by-step explanation:

x² - 4x - 1 = 0

b² - 4ac = (-4)² - 4(1)(1)

= 16 - 4

= 12

Since

b² - 4ac > 0

Therefore, the given equation will have real roots.

Quadratic formula

x = −b + √(b² − 4ac)

2a

x = −b − √(b² − 4ac)

2a

$\frac{4 + \sqrt{12} }{2} = \frac{4 +2 \sqrt{3} }{2} = 2 + \sqrt{3}$

$\frac{4 - \sqrt{12} }{2} = 2 - \sqrt{3}$