Question

if x = 3 and x = 0 are the zeroes of the polynomial (2x³ - 8x² + ax + b) , then find the value of a and b.

Answer 1

This is hard problem
please mark this as brainliest

Answer 2

$\mathbb{ SOLUTION }$ :

Let,
P(x) = 2x³ - 8x² + ax + b

Since,
x = 3 is a zero of the polynomial

$\therefore$ 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

=> -18 + 3a + b = 0

=> 3a + b = 18 _____(i)

Also,
x = 0 is also zero of the polynomial

$\therefore$ P(0) = 0

=> 2*(0)³ - 8*(0)² + a*0 + b = 0

=> 0 - 0 + 0 + b = 0

=> b = 0 ______(ii)

On putting = 0 in equation (i), we get

=> 3a + b = 18

=> 3a + 0 = 18

=> 3a = 18

=> a = 18 ÷ 3

=> a = 6

Hence,
a = 6
b = 0