Question

X²+6x+1=0 using quadratic formula

Answer 1

Required Answer:-

Given:

• x² + 6x + 1 = 0

To Find:

• The roots of the given equation using quadratic formula.

Solution:

Given equation,

⟹ x² + 6x + 1 = 0

Here,

• a (coefficient of x²) = 1
• b (coefficient of x) = 6
• c (coefficient of x⁰) = 1

Roots of a quadratic equation are given by the formula,

⟹ x₁,₂ = (-b ± √∆)/2a

Where,

⟹ ∆ = b² - 4ac (Also called discriminant)

Calculate the value of discriminant,

b² - 4ac

= 6² - 4 × 1 × 1

= 36 - 4

= 32

Therefore,

⟹ x₁,₂ = (-6 ±√32)/2

⟹ x₁,₂ = (-6 ± 4√2)/2

⟹ x₁,₂ = -3 ± 2√2

⟹ x = -3 + 2√2 and -3 - 2√2

Hence, the roots of the given equation are -3 + 2√2 and -3 - 2√2.

Answer:

• The roots of the given equation are -3 + 2√2 and -3 - 2√2.