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Question 7
Let r and c be real numbers. If r and -r are roots of $$5x^{3} + cx^{2} - 10x + 9 = 0$$, then c equals
Solution
Let the roots of the given equation $$5x^{3} + cx^{2} - 10x + 9 = 0$$ be r, -r and p
r - r + p = $$-\frac{c}{5}$$
p = $$-\frac{c}{5}$$ ...... (1)
$$-r^2-pr+pr=-2$$
$$r^2=2$$ ...... (2)
$$-r^2p=-\frac{9}{5}$$
$$p=\frac{9}{10}$$ ...... (3)
Substituting p in (1), we get
$$\frac{9}{10}=-\frac{c}{5}$$
$$-\frac{9}{2}=c$$
The answer is option A.
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