Question

Find the quadratic equation whose roots are
$(6 + \sqrt5) \\ (6 - \sqrt{5)}$
​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The required quadratic equation is x² - 12x + 31 = 0

Step-by-step explanation:

Let α and β be the roots of the quadratic equation.

Therefore,

α = 6 + √5

β = 6 - √5

∴ Sum of the roots

= α + β

= 6 + √5 + 6 - √5

= 12

∴ Product of the roots

= α×β

= (6 + √5)(6 - √5)

= (6)² - (√5)²

= 36 - 5

= 31

∴ Required Quadratic Equation:-

x² - (Sum of the roots)x + Product of the roots = 0

=> x² - (α + β)x + αβ = 0

=>x² - 12x + 31 = 0

Hence, the quadratic equation is x² - 12x + 31 = 0

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