Question

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

Answer 1

Answer:

The other root is 1-√2

Step-by-step explanation:

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

Then the next root must be 1-√2

If a quadratic equation with rational coefficients, the all coefficients are rational numbers.

Check the roots

Sum of roots =1+√2 + 1-√2  = 2

Products of roots = (1+√2 )(1-√2 ) = 1 - 2  = -1

Quadratic equation

Therefore the quadratic equation be,

x^2−2x−1=0.

Answer 2

Answer:

1-√2

Step-by-step explanation:

∴ given the one root is 1+√2 so let the other root is 1-√2.

Sum of the roots :

1+√2+1-√2

1+1

2

Products of the roots :

(1+√2)(1-√2)

1-(√2)²

1-2

-1

We got sum and products of the root so we can make the equation

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

x²-2x-1=0

Let's see it is correct or not!

x²-2x-1=0

Here, a=1, b=-2, c=-1

x = -b±√b²-4ac/2a

x = -(-2)±√(-2)²-4.1.(-1)/2.1

x = 2±√4+4/2

x = 2±√8/2

x = 2±2√2/2

x = 2(1±√2)/2

x = 1±√2

Hence, it is correct. The one root is 1+√2 then other root will be 1-√2