Question

If a, b be the roots of x² + px + q = 0 and a + h, b + h are the roots of x² + rx + s = 0 then-

• A. $\frac{p}{r}$= $\frac{q}{s}$
• B. 2h = $\left\lbrack \frac{p}{q} + \frac{r}{s} \right\rbrack$
• C. p² – 4q = r² – 4s
• D. pr² = qs²

Answer 1

Answer: (C)

p² – 4q = r² – 4s

Answer 2

a, b ® x² + px + q = 0

a + h, b + h ® x² + rx + s = 0

|a – b| = |(a + h) – (b + h)|

Ž $\frac{\sqrt{D_{1}}}{|a_{1}|}$= $\frac{\sqrt{D_{2}}}{|a_{2}|}$Ž $\frac{p^{2}–4q}{1}$ = $\frac{r^{2}–4s}{1}$

Ž p²–4q = r² – 4s