If , , and are the real roots of , then the equation…

MATHEMATICS · Multi correct · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

If ∣a∣<∣b∣|a|<|b|, b−a<1b-a<1, and a,ba,b are the real roots of x2−∣α∣x−∣β∣=0x^2-|\alpha|x-|\beta|=0, then the equation log⁡∣b∣∣xa∣−1=0\log_{|b|}\left|\frac{x}{a}\right|-1=0 has (1) one root lying in the interval (−∞,a)(-\infty,a) (2) one root lying in the interval (b,∞)(b,\infty) (3) one positive root (4) one negative root

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