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If f(x) is a polynomial of degree 4 wi...

If ` f(x) ` is a polynomial of degree 4 with rational coefficients
and touches x - axis at ` (sqrt(2) , 0 )` , then for the equation
` f(x) = 0`,

A

sum of roots is ` 4 sqrt(3)`

B

sum of roots is 0

C

product of roots is - 4

D

product of roots is 4.

Text Solution

Verified by Experts

The correct Answer is:
2,4,
It is given that f(x) touches x - axis at ` (sqrt(2), 0 )` . So, two roots are
` sqrt(2), sqrt(2).`
since coefficients are rational, other roots must be sqrt(2), sqrt(2).`
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