Question

heya answer this que​

Answer 1

AnsWer :

• a = - 5.
• b = 0.

QuestioN :

If x = 0 and x = - 1 are the roots ( zeros ) polynomial f ( x ) 2x² - 3x² + ax + b, find the value of a and b

To Find :

The value of a and b.

SolutioN :

We have,

$\tt \dagger \: \: \: \: \: \fbox{ 2 {x}^{3} - 3 {x}^{2} + ax + b}$

Let,

• f( x ) = 0.

$\tt : \implies f(0) = 2 {x}^{3} - 3 {x}^{2} + ax + b$

$\tt : \implies 0 = 2 {(0)}^{3} - 3 {(0)}^{2} + a \times0 + b$

$\tt : \implies b = 0.$

Now,

• f ( x ) = - 1.

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

$\tt : \implies 0 = - 2 - 3 - a + b.$

$\tt : \implies 0 = - 5 - a$

$\tt : \implies a =- 5.$

Therefore, the value of a = - 5, b = 0.

Answer 2

✰✰ ANSWER ✰✰

☛Putting x = 0 : -

$\longmapsto\tt{{2x}^{3}-{3x}^{2}+ax+b}$

$\longmapsto\tt{2{(0)}^{3}-3{(0)}^{2}+a(0)+b=0}$

$\longmapsto\tt{0-0+0+b=0}$

$\pink\longmapsto\:\large\underline{\boxed{\bf\red{b}\green{=}\orange{0}}}$

Now ,

☛Putting x = -1 : -

$\longmapsto\tt{{2x}^{3}-{3x}^{2}+ax+b}$

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

$\longmapsto\tt{2(-1)-3(1)-1a+0=0}$

$\longmapsto\tt{-2-3-a=0}$

$\longmapsto\tt{-a=5}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{a}\orange{=}\purple{-5}}}$

➥So, Value of a is -5 and value of b is 0...