Question 43
If one of the roots of $$ax^2+bx+c=0$$ is half of the other root, then which of the following conditions must be true?
Solution
If the root is p then the sum of the roots = 3p/2 = -b/a => p=-2b/3a, and product of roots is $$p^2/2=c/a$$. $$(-2b/3a)^2=2c/a $$=>$$ 4b^2/9a^2 = 2c/a => 2b^2=9ac$$
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