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


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