Q. 1 G3.7( 3 Votes )

Write each polyno

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

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