The equation `10x^(4)-3x^(2)-1=0` has

Options

A. no rational but three irrational roots
B. one rational and two irrational roots
C. no real roots
D. three rational roots

Answer

A

Explanation

If possible, let `(p)/(q)` be a rational roots of `x^(3) - 3x + 1 = 0`. Then, p is a factor of the constant term i.e. 1 and q is a factor of coefficient of `x^(3)` i.e. 1.
`therefore" "p = +- 1 and q = +- 1 rArr (p)/(q) = 1, -1`
But, 1 and -1 do not satisfy the given equation.
Hence, the given equation has no rational roots.