Q. 1 G3.7( 3 Votes )

# Write each polyno

Answer :

Given, p(x) = 2x2 – 5x + 2

Now, we need to write the given polynomial as a product of first degree polynomial and p(x) = 0

2x2 – 5x + 2 can be written as 2(x2 x + 1)

Now, we will find out the factors for x2 x + 1

x2 x + 1 is in the form x2 – (a + b)x + ab and (x – a)(x – b) are the factors

coefficient on either side of the polynomial is same and a + b = and ab = 1

we know that (a + b)2 –(a – b)2 = 4ab

(a + b)2 – 4ab = (a – b)2 – 4(1) = (a – b)2 – 4 = (a – b)2 = (a – b)2 = (a – b)2

a – b = a – b = We need to find out the values of a and b by solving (a + b) + (a – b) and (a + b) – (a – b)

we take a – b = (a + b) + (a – b) = + 2a = a = 2

(a + b) – (a – b) =  2b = b = we get a = 2 and b = And if we take a – b = – we get as follows

(a + b) + (a – b) = + (– )

2a = a = (a + b) – (a – b) =  2b = b = 2

a = and b = 2

So, we have 2(x – )(x – 2)

(2x – 1)(x – 2)

(2x – 1)(x – 2) are the factors

p(x) = 0 if (2x – 1) is 0 and (x – 2) is 0

(2x – 1) = 0

2x = 1

x = Substitute, x = in 2x2 – 5x + 2 = 2( 2 – 5( + 2 =  + 2 = 0

(x – 2) = 0

x = 2 substitute, 2x2 – 5x + 2 = 2(2)2 – 5(2) + 2 = 8 – 10 + 2 = 0

Hence, (2x – 1)(x – 2) are the first degree factors of the polynomial and and 2 are the solution of the given polynomial 2x2 – 5x + 2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

A square ground hKerala Board Mathematics Part-1

Write each polynoKerala Board Mathematics Part-2

Write each polynoKerala Board Mathematics Part-2

Write each polynoKerala Board Mathematics Part-2

Write each polynoKerala Board Mathematics Part-2

Write each polynoKerala Board Mathematics Part-2

By adding a numbeKerala Board Mathematics Part-2

By adding a numbeKerala Board Mathematics Part-2

Find a third degrKerala Board Mathematics Part-2

Find a second degKerala Board Mathematics Part-2