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X²+6x+1=0 using quadratic formula

Answer»

Required Answer:-

Given:

  • x² + 6x + 1 = 0

To Find:

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.


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