The roots of the equation, (x-a)(x-b)=a2-2 b2 are real and distinct for all a0, provided

Question

The roots of the equation, (x-a)(x-b)=a2-2 b2 are real and distinct for all a>0, provided (A) - a ≤ b <(5/7) a (B)  -a<b<(5/7) a (C) - a < b ≤ (5/7) a (D) -2 a < b <(7/5) a

Tardigrade Admin · Accepted Answer

Correct answer is (b) -a<b<(5/7) a

Q. The roots of the equation, $(x - a) (x - b) = a^{2} - 2 b^{2}$ are real and distinct for all $a > 0$ , provided

- a $\leq$ b $< \frac{5}{7}$ a

$- a < b < \frac{5}{7} a$

- a $<$ b $\leq \frac{5}{7}$ a

-2 a $<$ b $< \frac{7}{5}$ a

Correct answer is (b) $- a < b < \frac{5}{7} a$

Q. The roots of the equation, (x−a)(x−b)=a2−2b2 are real and distinct for all a>0, provided

- a ≤ b <75​ a

−a<b<75​a

- a < b ≤75​ a

-2 a < b <57​ a