Answer :

Given, p(x) = 6x2 – 7x + 2


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


6x2 – 7x + 2 can be written as 6(x2 x + ) = 6(x2 x + )


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


x2 x + 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 =


we know that (a + b)2 –(a – b)2 = 4ab


(a + b)2 – 4ab = (a – b)2


– 4() = (a – b)2


= (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 = =


(a + b) – (a – b) =


2b =


b =


we get a = and b =


And if we take a – b = – we get as follows


(a + b) + (a – b) = + (– )


2a =


a =


(a + b) – (a – b) = – (– )


2b =


b =


a = and b =


So, we have 6(x – )(x – )


(6x – )( x – )


(6x – 3)(x – )


(6x – 3)(x – ) are the factors


p(x) = 0 if (6x – 3) is 0 and (x – ) is 0


(6x – 3) = 0


6x = 3


x = =


Substitute, x = in 6x2 – 7x + 2 = 6(2 – 7( + 2 = + 2 = 0


(x – ) = 0


x = substitute, 6x2 – 7x + 2 = 6()2 – 7() + 2 = + 2 = 0


Hence, (6x – 3)(x – ) are the first degree factors of the polynomial and and are the solution of the given polynomial 6x2 – 7x + 2


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