find zero of polynomial x2-8x+12 and verify relationship between zeros and coefficent of polynomial
Answers
Step-by-step explanation:
The first term is, x^2 its coefficient is 1 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is +12
Step-1 : Multiply the coefficient of the first term by the constant 1 • 12 = 12
Step-2 : Find two factors of 12 whose sum equals the coefficient of the middle term, which is -8 .
-6 + -2 = -8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -2
x2 - 6x - 2x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
2 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x-2) • (x-6)
Which is the desired factorization
x= 2 or x= 6.
relationship between zeros and coefficent of polynomial..
α+β = -b/a.
αβ =c/a.
sum of zeroes =-b/a
so,2+6 = -(-8)/1
8=8.
product of zeroes =c/a .
(2)(6) = 12/1.
12 = 12.
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