Question

if 0 and 1 are the zeroes of the polynomial f(x) = 2x cube - 3x square + ax +b, find the values of a and b. ​

Answer 1

Answer:

put the value of zeros in f (x)

Answer 2

Step-by-step explanation:

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

$let \: 0 \: be \: the \: zero \: of \: the \: polynomial$

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

$= 0 - 0 + 0 + b$

$= b$

$let \: 1 \: be \: the \: other \: zero \: of \: the \: polynmial$

$2( {1}^{3} ) - 3( {1}^{2} ) + a(1) - b$

$2 - 3 + a + b$

$a + b = 1$

$a = b + 1$

$a + b = 1 + b\: this \: is \: because \: roots \: are \: equal \: and \: the \: values \: them \: are \: equal \:$

$b \: and \: b \: get \: cancelled \: on \: both \: sides \: and \: the \: value \: of \: a \: is \: 1$