Question

# Let $$b = a + c$$. Then the equation $$ax^2+bx+c=0$$ has equal roots, if

A
a=c
B
a=c
C
a=2c
D
a=2c

Solution

## The correct option is B $$a=c$$Given $$b=a+c$$ and equation $$ax^2+bx+c=0$$ has equal rootsFor equal roots$$D=0$$$$b^{2}=4ac$$$$b=a+c$$$$(a+c)^{2}=4ac$$$$a^{2}+c^{2}+2ac=4ac$$$$a^{2}+c^{2}-2ac=0$$$$(a-c)^{2}=0$$$$\therefore\ \boxed{a=c\ }$$Mathematics

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