Question

verify 1/2 and 1 are zroes of the Polynomial (p(x) = 2x² - 3x +1)​

Answer 1

Let f(x)=x

3

−2x

2

−5x+6

3,−2 and 1 are the zeroes of the polynomial ( given )

Therefore,

f(3)=(3)

3

−2(3)

2

−5(−2)+6

=27−18−15+6

=0

f(−2)=(−2)

3

−2(−2)

2

−5(−2)+6

−8−8+10+6

=0

f(1)=(1)

3

−2(1)

2

−5(1)+6

=1−2−5+6

=0

Verify relations :

General form of cubic equation :ax

3

+bx

2

+cx+d

now ,

Consider α=3,β=−2 and y=1

α+β+y=3−2+1=2=−b/a

αβ+βy+αy=3(−2)+(−2)(1)+1(3)=−5=c/a

and αβy=3(−2)(1)=−6=−d/a

Answer 2

Answer:

(2x-1)(x-1)

Step-by-step explanation:

p=2x^2 -3x+1
p=2x^2-(2+1)x+1
p=2x^2-2x-x+1
p=2x(x-1)-1(x-1)
p=(2x-1)(x-1)