Question

if 0 and 1 are the zeros of the polynomial f of x is equal to 2 x cube minus 3 X square + a x + b find the values of a and b

Answer 1

Heya !!



Given that : 0 and 1 are the two zeroes of the given polynomial.

P ( X ) = 2X³ - 3X² + AX + B




P ( 0 ) = 2 × (0)³ - 3 × (0)² + A × 0 + B




=> 0 - 0 + 0 + B = 0




=> B = 0




And,



Also , X = 1

P ( 1) = 2 × (1)³ - 3 × (1)² + A × 1 + B





=> 2 - 3 + A + B = 0




=> -1 + A + 0 = 0





=> A = 1


Hence,


A = 1 and B = 0.

Answer 2

Given,

$polynomial \: f(x) = 2 {x}^{3} - 3 {x}^{2} + ax + b$

0 and 1 are the zeros of the polynomial.

To find out,

Find the values of a and b.

Solution:

If the value of x = 0.

then,

$f(0) = 2 {(0)}^{3} - 3 {(0)}^{2} + a(0) + b$

$0 = 2(0) - 3(0) + 0 + b$

$0 = 0 - 0 + 0 + b$

$b \: = 0$

Therefore the value of b is 0.

If the value of x = 1.

then,

$f(1) = 2 {(1)}^{3} - 3 {(1)}^{2} + a(1) + 0 \: (since \: b \: = 0)$

$0 = 2(1) - 3(1) + a + 0$

$0 = 2 - 3 + a$

$0 = - 1 + a$

$a = 1$

Therefore the value of a is 1.