Q. 1 B5.0( 3 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


P(x) = 0 if (x + 3) is 0 and (x + 4) is 0


x + 4 = 0


x = – 4


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


And x + 3 = 0


x = – 3


x2 + 7x + 12 = (– 3)2 + 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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