Multiple choice

If $ \alpha, \beta $ are the roots of $ ax^{2}+bx+c=0 $; $ \alpha+h,\beta+h $ are the roots of $ px^{2}+qx+r=0 $; and $ D_{1},D_{2} $ are the respective discriminants of these equations, then $ D_{1}:D_{2} $ is

  1. $ \displaystyle \frac{a^{2}}{p^{2}} $
  2. $ \displaystyle \frac{b^{2}}{q^{2}} $
  3. $ \displaystyle \frac{c^{2}}{r^{2}} $
  4. $1$
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A Correct answer
Explanation

If roots of ax^2+bx+c=0 are alpha, beta, then D1 = b^2 - 4ac. If roots of px^2+qx+r=0 are alpha+h, beta+h, the equation is p(x-h)^2 + q(x-h) + r = 0. Expanding this, the discriminant D2 = q^2 - 4pr. Given the relationship between roots, D1/D2 = a^2/p^2.

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