Question

please do it ,
Only 1st equation

Answer 1

p(x) = 2x³ + x² - 5x + 2

p(1/2) = 2 × (1/2)³ + (1/2)² - 5×1/2 + 2

= 2×1/8 + 1/4 - 5/2 + 2

= 1/4+1/4 - 5/2 + 2/1

= +10-10/4

= 0

yes it is the zeroes of this polynomial

p(1) = 2 ×(1)³ + (1)²-5×1 + 2

= 2+1-5+2

=5-5

=0

yes it is the zeroes of this polynomial

p(-2) = 2 ×(-2)³+(-2)²-5×-2 + 2

= -16+4+10+2

=-16+16

= 0

yes it is also the zeroes of this polynomial

1/2 , 1 . -2 are the zeroes of this polynomial

α = 1/2 , β = 1 , y = -2 ( there is no the sign of gamma so I used symbol y)

sum of the zeroes = -b/a (coefficient of x² / coefficient of x³)

α + β + y = -b/a

1/2 + 1+(-2) = -1/2

3-4/2 = -1/2

-1/2 =-1/2

sum of product of zeroes = c/a (constant term /coefficient of x³)

α×β + β×y + y×α = -5/2

1/2×1 + 1×(-2) + (-2)×1/2 = -5/2

1/2 -2-1 = -5/2

1-4-2/2 = -5/2

1-6/2 = -5/2

-5/2 = -5/2

)

product of zeroes = -d/a (constant term /coefficient of x³

α×β×y = -d/a

1/2×1×-2 = -2/2

-1 = -1

hence, verified

Hope it will be helpful for you