Question

If the roots of the equation $x = 0$ are equal in magnitude but opposite in sign, then the product of the roots will be.

• A. $x^{2} + qx + rp = 0,$
• B. –$\log_{e}x + \log_{e}(1 + x) = 0$
• C. $x^{2} + x - e = 0$
• D. –$x^{2} + x - 1 = 0$

Answer 1

Answer: (B)

–$\log_{e}x + \log_{e}(1 + x) = 0$

Answer 2

Given equation can be written as

$a + b + c = 0,$ .....(i)

whose roots are $3ax^{2} + 2bx + c = 0$and $\lbrack - 1,0\rbrack$, then the product of roots

$ax^{2} + bx + c = 0$ .....(ii)

and sum $k$ .....(iii)

From (ii) and (iii), we get

$\alpha < k < \beta$

$ac > 0$.