find the zeroes of 9x2 + 3x - 2:and verify the relation between the zeroes and its coefficients
Answers
Step-by-step explanation:
Factoring 9x2+3x-2
The first term is, 9x2 its coefficient is 9 .
The middle term is, +3x its coefficient is 3 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 9 • -2 = -18
Step-2 : Find two factors of -18 whose sum equals the coefficient of the middle term, which is 3 .
-3 + 6 = 3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 6
9x2 - 3x + 6x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (3x-1)
Add up the last 2 terms, pulling out common factors :
2 • (3x-1)
Step-5 : Add up the four terms of step 4 :
(3x+2) • (3x-1)
Which is the desired factorization
3x+2 =0 (or) 3x-1 = 0 .
3x= -2 (or) 3x= 1.
x= -2/3 (or) x= 1/3.
relation between the zeroes and its coefficients is provided in the attachment....
The two zeroes are 2/3 and -1/3
-b/a=1/3=the sum of zeroes
c/a=-2/9=the product of zeroes