AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

State if the statement is true or false: The factorised form of $1 − 6 x + 9 x 2$ is $(3 x − 1) 2$ .

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The given quadratic equation

1 − 6 x + 9 x 2

can be written in the standard form as follows,

9 x 2 + 6 x + 1

Now, it is of the form

a x 2 + b x + c

, where a=9, b=6 and c=1.
In order to factorize these types of equations, we need to find two factors, say p and q such that the following two conditions are satisfied,

a c = p q

p + q = b

According to the above conditions, the product of first and last constant term of the expression will be

9 × 1 = 9

.
Next, we will have to find the factors of product, i.e.,

− 24

in such a way that their sum or difference is equal to the middle term. So, we have the factors as

− 3 × − 3 = 9

which is the product of the first and last terms of the equation, while their sum, i.e.,

− 3 + (− 3) = − 6

is the middle term.
Now, we will factorize the expression using the factors and splitting the middle term as follows,

9 x 2 − 6 x + 1 = 9 x 2 − 3 x − 3 x + 1 = 3 x (3 x − 1) − 1 (3 x − 1) = (3 x − 1) (3 x − 1) = (3 x − 1) 2

So, the factored form of

3 + 23 x − 8 x 2

(3 x − 1) 2

.
Hence, the given statement is true.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!