Q. 1 H5.0( 1 Vote )

# Write each polyno

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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