Multiple choice

If the roots of the equation $px^{2} + qx + r = 0$ are in the ratio $l : m$, then $(l + m)^{2} pr = lm\ q^{2}$. is ?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For roots in ratio l:m, the condition is (l+m)^2 / lm = b^2 / ac. Here a=p, b=q, c=r. So (l+m)^2 / lm = q^2 / pr, which rearranges to (l+m)^2 * pr = lm * q^2.

AI explanation

Let the roots be lm and mm, making their sum lm + mm = -q/p and their product lm^2 = r/p. From the sum, q^2/p^2 = m^2(l+m)^2, and from the product, r/p = lm^2. Dividing the squared sum by the product gives q^2/pr = (l+m)^2/l. Multiplying by pr(l+m)^2 gives lm q^2 = (l+m)^2 pr. This proves the statement is True.

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