2x^2-7x+6x-21 find zero of polynomial and verify the answer
Answers
Step-by-step explanation:
2x^2-7x+6x-21= 0. =》 2x^2-x-21 =0.
The first term is, 2x2 its coefficient is 2 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -21
Step-1 : Multiply the coefficient of the first term by the constant 2 • -21 = -42
Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is -1 .
-7 + 6 = -1
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 6
2x2 - 7x + 6x - 21
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-7)
Add up the last 2 terms, pulling out common factors :
3 • (2x-7)
Step-5 : Add up the four terms of step 4 :
(x+3) • (2x-7)
Which is the desired factorization
x+3 =0 (or) 2x-7 = 0.
x= -3 (or) x= 7/2
verification
to verify weather they are zeroes or not substitute x= -3 (or) x= 7/2 in the given equation
if the value of the equation becomes zero then they are the zeroes of the equation.....
2x^2-x-21 is the given equation....
2(-3)^2-(-3)-21=0
=》2(9)+3-21 =0.
=》18+3-21=0
=》21-21=0.
0=0.
now substitute x= 7/2 in the given equation..
2x^2-x-21
=》2(7/2)^2-(7/2)-21=0
=》2(49/4)-7/2-21=0
=》49/2-7/2-21=0.
=》[(49-7)/2]-21 =0.
=》(42/2)-21 =0.
=》21-21=0.
0= 0.
therefore x= -3 (or) x= 7/2 are the zeroes of the 2x^2-7x+6x-21= 0.