Question

If $b=a+c$ and the equation $a{x}^2+bx+c=0$ has equal roots, then

• A. $a=c$
• B. $a=-c$
• C. $a=2c$
• D. $a=-2c$

Answer 1

The correct option is A $a=c$

Given quadratic equation is $a{x}^2+bx+c=0$

Also given $b=a+c$

We know that, when a given equation have equal roots, then its discriminant is always equal to be zero.

Therefore, $D=0$

$\Rightarrow b^2-4ac=0$

$\Rightarrow b^2=4ac$

$\Rightarrow (a+c{)}^2=4ac$

$\Rightarrow a^2+2ac+c^2=4ac$

$\Rightarrow a^2-2ac+c^2=0$

$\Rightarrow (a-c{)}^2=0$

$\Rightarrow a-c=0$

$\Rightarrow a=c$

Hence, option A is correct.