Question

If 1 + √2 is a root of a quadratic equation with rational coefficients, write its other root.

Answer 1

other root is 1 - √2 If 1 + √2 is a root of a quadratic equation with rational coefficients

Step-by-step explanation:

If 1 + √2 is a root of a quadratic equation with rational coefficients

then other roots would be 1 - √2

as sum of roots & products of roots is rational

equation would be

(x - ( 1 + √2))(x - (1 - √2))

= x²  - x( 1 - √2 + 1 + √2) + ( 1 - 2)

= x² - 2x - 1

x² - 2x - 1  is the Quadratic equation

and 2nd root is 1 - √2

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