if 1+√2 is a root of the quadratic equation with rational co efficient write are other roots?
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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
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