The quadratic equation a x^2-4 a x+2 a+1=0 has repeated roots, if… - Vidyadip

MCQ

The quadratic equation $a x^2-4 a x+2 a+1=0$ has repeated roots, if $a=$

A
$0$
✓
$1 / 2$
C
$2$
D
$4$

✓

Answer

Correct option: B.

$1 / 2$

The roots are said to be repeated, if
$B^2-4 A C=0 $
$\Rightarrow(-4 a)^2-4 \times a \times(2 a+1)=0$
$\Rightarrow 16 a^2-4 a(2 a+1)-0$
$ \Rightarrow 16 a^2-8 a^2-4 a-0$
$\Rightarrow 8 a^2-4 a=0 $
$\Rightarrow a(8 a-4)=0 $
$\Rightarrow a=0 \text { or } 8 a-4=0$
$\therefore a=1 / 2 \ (\because a \neq 0)$

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 Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

The area of a square is the same as the area of a circle. Their perimeters are in the ratio:

A vertical stick $1.8m$ long casts a shadow $45\ cm$ long on the ground. At the same time, what is the lenght of the shadow of a pole $6m$ high?

The area of a circle whose area and circumference are numerically equal, is:

A quadratic polynomial whose zeroes are $\frac{2}{5}$ and $\frac{-1}{5}$is

If $\cos\text{A}+\cos^2\text{A}=1$ then $\sin^2\text{A}+\sin^4\text{A}=?$

The LCM of $ 2^3 \times 3^2 $ and $ 2^2 \times 3^3 $

If $x = -y$ and $y > 0,$ which of the following is wrong ?

If the surface area of a sphere is $616 \ cm^2$, its diameter is

A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is:

Two poles of height $6m$ and $11m$ stand vertically upright upright on a plane ground. If distance between their fiit is $12m$ then the distance between their tops is :