If the equation $a(b-c)x^2+b(c-a)x+c(a-b)=0$ has equal roots, where $a+c=15$ and $b=\frac{36}5$, then $a^2+c^2$ is equal to

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] The coefficients sum to $0$, so $x=1$ is a root; equal roots means both are $1$ and the product $\frac{c(a-b)}{a(b-c)}=1$. This gives $2ac=b(a+c)$, so $ac=\frac{36}5\cdot\frac{15}2=54$. $a^2+c^2=15^2-2\cdot54=117$. Answer: 117.

Q. If the equation $a(b-c)x^2+b(c-a)x+c(a-b)=0$ has equal roots, where $a+c=15$ and $b=\frac{36}5$, then $a^2+c^2$ is equal to

Explanation

Reviewed by Dr. Abubacker

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