QJEEM20Maf09f: JEE Main 2020 Mathematics - Class 11 JEEM20Maf09f Solution: Let a , b, c , d and p be any non zero distinct real numbers…

(a² + b² + c²)p² – 2(ab + bc + cd)p + (b² + c² + d²) = 0

$$\Rightarrow$$ (a²p² + 2abp + b² ) + (b²p² + 2bcp + c² ) + (c² p² + 2cdp + d²) = 0

$$\Rightarrow$$ (ab + b)² + (bp + c)² + (cp + d)² = 0

Note : If sum of two or more positive quantity is zero then they are all zero.

$$\therefore$$ ap + b = 0 and bp + c = 0 and cp + d = 0

p = $$-\frac{b}{a}$$ = $$-\frac{c}{b}$$ = $$-\frac{d}{c}$$

or $$\frac{b}{a}$$ = $$\frac{c}{b}$$ = $$\frac{d}{c}$$

$$\therefore$$ a, b, c, d are in G.P.