Question

If x = 2 and x = 0 are zeros of the polynomial 2x^3 - 5x^2 + px + b , then find the value of p and b

Answer 1

2(2^3)-5(2^2)+2p+b=0
16-20+2p+b=0
2p+b=4. This is first equation
2(0^3)-5(0^2)+p(0)+b=0
0-0+0+b=0
Therefore b=0
Substitute in First equation
2p+b=4
2p+0=4
P=4/2
Therefore p=2

Answer 2

Answer:

The value of p and b is 2 and 0 respectively.

Step-by-step explanation:

$\text{Given that x = 2 and x = 0 are the zeroes polynomial }P(x)=2x^3 - 5x^2 + px + b$

$\text{we have to find the the value of p and b}$

As x = 2 and x = 0 are the zeroes polynomial therefore by remainder theorem

P(2)=0 and P(0)=0

P(0)=0

$2(0)^3-5(0)^2+p(0)+b=0$

$0-0+0+b=0$

$b=0$

P(2)=0

$2(2)^3-5(2)^2+p(2)+b=0$

$16-20+2p+0=0$

$-4+2p=0$

$p=\frac{4}{2}=2$

Hence, the value of p and b is 2 and 0 respectively.