Question

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

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

Answer 1

Answer: (A)

$a=c$

Given $b=a+c$ and equation $a{x}^2+bx+c=0$ has equal roots

For equal roots

$D=0$

$b^2=4ac$

$b=a+c$

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

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

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

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

$\therefore a=c$