Question

The quadratic equation whose one rational root is `3 + sqrt2` is

Options

• x² – 7x + 5 = 0

• x² + 7x + 6 = 0

• x² – 7x + 6 = 0

• x² – 6x + 7 = 0

Answer 1

x² – 6x + 7 = 0

Explanation:

∵ one root is `3 + sqrt2`

∴ other root is `3 - sqrt2`

∴ Sum of roots = `3 + sqrt2 + 3 - sqrt2` = 6

Product of roots = `(3 + sqrt2) (3 - sqrt2)`

= `(3)^2 - (sqrt2)^2`

= 9 – 2

= 7

∴ Required quadratic equation is x² – 6x + 7 = 0.