Q. 1 A4.8( 5 Votes )

Write each polyno

Answer :

Given, p(X) = x2 – 7x + 12


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


x2 – 7x + 12 = 0


The given equation can be written as follows


(x – 4)(x – 3) = 0


Since, we know that x2 – 7x + 12 can be written as (x – a)(x – b)


x2 – 7x + 12 = x2 – (a + b)x + ab


coefficient on either side of the polynomial is same and a + b = 7 and ab = 12


we must find two numbers that satisfy a + b and ab we get, 4 and 3 as the numbers


(x – 4)(x – 3) are the product of first degree polynomial


Substitute x = 4 and x = 3, We get p(x) as 0


x2 – 7x + 12 = 42 – 7(4) + 1 2 = 16 – 28 + 12 = 0


x2 – 7x + 12 = 32 – 7(3) + 12 = 9 – 21 + 12 = 0


Hence, (x – 4)(x – 3) are the first degree factors of the polynomial and 4, 3 are the solutions of the given polynomial x2 – 7x + 12


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