Q. 1 C5.0( 1 Vote )

Write each polynomial below as a product of first degree polynomials. Write also the solutions of the equation p(x) = 0 in each.

p(x) = x2 – 8x + 12

Answer :

Given, p(X) = x2 – 8x + 12


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


x2 – 8x + 12 = 0


The given equation can be written as follows


(x – 6)(x – 2) = 0


Since, we know that x2 – 8x + 12 can be written as (x – a)(x – b)


x2 – 8x + 12 = x2 – (a + b)x + ab


coefficient on either side of the polynomial is same and a + b = 8 and ab = 12


we must find two numbers that satisfy a + b and ab we get, 6 and 2 as the numbers


(x – 6)(x – 2) are the product of first degree polynomial


P(x) = 0 if (x – 6) is 0 and (x – 2) is 0


x – 6 = 0


x = 6


x2 – 8x + 12 = 62 – 8(6) + 12 = 36 – 48 + 12 = 0


And x – 2 = 0


x = 2


x2 – 8x + 12 = 22 – 8(2) + 12 = 4 – 16 + 12 = 0


Hence, (x – 6)(x – 2) are the first degree factors of the polynomial and 6, 2 are the solutions of the given polynomial x2 – 8x + 12


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