118477
Let \(p, q \in \mathbb{R}\) and \((1-\sqrt{3} i)^{200}=2^{199}(p+i q), i=\) \(\sqrt{-1}\) Then \(p+q+q^2\) and \(p-q+q^2\) are roots of the equation.
118457
Roots of the equation \(x^2+b x-c=0(b, c>0)\) are
1 Both positive
2 Both negative
3 Of opposite sign
4 None of these
Explanation:
C Since b, c \(>0\) Therefore \(\alpha+\beta=-b\lt 0\) and \(\alpha \beta=-c\lt 0\) Since product of the roots is (-ve) therefore roots must be of opposite sign.
118477
Let \(p, q \in \mathbb{R}\) and \((1-\sqrt{3} i)^{200}=2^{199}(p+i q), i=\) \(\sqrt{-1}\) Then \(p+q+q^2\) and \(p-q+q^2\) are roots of the equation.
118457
Roots of the equation \(x^2+b x-c=0(b, c>0)\) are
1 Both positive
2 Both negative
3 Of opposite sign
4 None of these
Explanation:
C Since b, c \(>0\) Therefore \(\alpha+\beta=-b\lt 0\) and \(\alpha \beta=-c\lt 0\) Since product of the roots is (-ve) therefore roots must be of opposite sign.
