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

MCQ

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

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

✓

Answer

Correct option: B.

$a = c$

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from MODEL PAPER 8 (STANDARD)→MODEL PAPER 8 (STANDARD) — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

If $u_i=\frac{x_i-25}{10}, \Sigma f_i u_i=20, \Sigma f_i=100$, then $\bar{x}=$

→

Match the following columns:

	Column $I$		Column $II$
$a.$	A solid metallic sphere of radius $8\ cm$ is melted and the material is used to make solid right cones with height $4\ cm$ and base radius of $8\ cm$. How many cones are formed?	$q.$	$8$
$b.$	A $20 - m -$ deep well with diameter $14m$ is dug up and the earth from digging is evenly spread out to form a platform $44m$ by $14m$. The height of the platform is $........ m.$	$s.$	$5$
$c.$	A sphere of radius $6 \ cm$ is melted and recast in the shape of a cylinder of radius $4\ cm$. Then, the height of the cylinder is $......... \ cm.$	$p.$	$18$
$d.$	The volumes of two spheres are in the ratio $64 : 27$. The ratio of their surface areas is $....... .$	$r.$	$16 : 9$