Question

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

Answer 1

Answer:

Value of a is 20/3 and value of b is 0.

Step-by-step explanation:

Given f(x)=$2 {x}^{3} - 8 {x}^{2} + ax + b.......(1)$

Two zeros of given polynomial are 3 and 0

If $2 {x}^{3} - 8 {x}^{2} + ax + b = 0$

Putting x=3 in the above equation and get

$2 \times {3}^{3} - 8 \times {3}^{2} + a \times 3 + b = 0$

$54 - 72 + 3a + b = 0 \\ 3a + b = 20.....(2)$

Putting x=0 in the above equation and get

$0 - 0 + 0 + b = 0$

Therefore b=0

From equation (2),

$3a + 0 = 20 \\ 3a = 20 \\ a = \frac{20}{3}$

So value of a is 20/3 and value of b is 0.