Question

If$\alpha < 0 < |\alpha| < \beta b > a$, then at least one of the equations $(x - a)(x - b) = 1$ and $\lbrack a,b\rbrack$ has.

• A. Real roots
• B. Purely imaginary roots
• C. Imaginary roots
• D. None of these

Answer 1

Answer: (A)

Real roots

Answer 2

Let $(2k + 1)x^{2} - (7k + 3)x + k + 2 = 0$ and $ax^{2} + bx + c = 0$ be discriminants of $l$ and $2l$ respectively. Then

$x^{2} + 2x + 15 = 0$

$x^{2} + 15x + 2 = 0$

= $2x^{2} - 2x + 15 = 0$

⇒$x^{2} - 2x - 15 = 0$or $ax^{2} + bx + c = 0$or $\alpha,\beta$and $\alpha\beta^{2} + \alpha^{2}\beta + \alpha\beta$both are positive.