Find the zeros of the quadratic polynomial and verify the relation between zeros and coefficients x2+25x+84
Answers
Answer:
x = -4
x = -21
Step-by-step explanation:
actoring x2+25x+84
The first term is, x2 its coefficient is 1 .
The middle term is, +25x its coefficient is 25 .
The last term, "the constant", is +84
Step-1 : Multiply the coefficient of the first term by the constant 1 • 84 = 84
Step-2 : Find two factors of 84 whose sum equals the coefficient of the middle term, which is 25 .
-84 + -1 = -85
-42 + -2 = -44
-28 + -3 = -31
-21 + -4 = -25
-14 + -6 = -20
-12 + -7 = -19
-7 + -12 = -19
-6 + -14 = -20
-4 + -21 = -25
-3 + -28 = -31
-2 + -42 = -44
-1 + -84 = -85
1 + 84 = 85
2 + 42 = 44
3 + 28 = 31
4 + 21 = 25 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 21
x2 + 4x + 21x + 84
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+4)
Add up the last 2 terms, pulling out common factors :
21 • (x+4)
Step-5 : Add up the four terms of step 4 :
(x+21) • (x+4)
Which is the desired factorization