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

MCQ

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

A
$a = -c$
B
$a = 2c$
✓
$a = c$
D
$a = -2c$

✓

Answer

Correct option: C.

$a = c$

Since, If $a x^2+b x+c=0$ has equal roots,
then $ b^2-4 a c=0 $
$ \Rightarrow(a+c)^2-4 a c=0\ [$Given : $b=a+c]$
$ \Rightarrow a^2+c^2+2 a c-4 a c=0 $
$ \Rightarrow a^2+c^2-2 a c=0 $
$ \Rightarrow(a-c)^2=0$
$\Rightarrow a - c = 0$
$\Rightarrow a = c$

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