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Question

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


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

The correct option is B $$a=c$$
Given $$b=a+c$$ and equation $$ax^2+bx+c=0$$ has equal roots

For 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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