Question

if x=3 and x=0 are the zeros of the polynomial 2x^3-8x^2+ax+b find a and b

Answer 1

Hey!!!!

We have,
p(x) = 2x³ - 8x² + ax + b

Zeros = 3,0

=> p(3) = 0
=> 2(3)³ - 8(3)² + a(3) + b = 0
=> 54 - 72 + 3a + b = 0
=> 3a + b = 18 ............. equation 1

=> p(0) = 0
=> 2(0) - 8(0) + a(0) + b = 0
=> b = 0

Using b in equation 1

=> 3a = 18
=> a = 6

Hope this helps

Answer 2

Hi...☺️

Here is your answer...✌️

LET
$p(x) = 2 {x}^{3} - 8 {x}^{2} + ax + b$

GIVEN THAT ,

x = 3 and x = 0 are zeros of polynomial

=> p(3) = 0

2(3)³ - 8(3)² + a(3) + b = 0

2×27 - 8×9 + 3a + b = 0

54 - 72 + 3a + b = 0

3a + b - 18 = 0

3a + b = 18 -----(1)

And,

=> p(0) = 0

2(0)³ - 8(0)² + a(0) + b = 0

=> b = 0

Putting b = 0 in eq(1)
We get

3a = 18

=> a = 18/3

=> a = 6

HENCE,

a = 6 , b = 0