Question

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

Answer 1

Answer:

hi I hope this answer will help u

Step-by-step explanation:

f(X)= 2x^3-3x^2+ ax+b

A). if X=0 is the root of f(X) then

f(0)=0

2(0)^3-3(0)^2+a(0)+b=0

b=0

B). of X=-1 then

f(-1)=0

2(-1)^3-3(-1)^2+a(-1)+b=0

-2-3-a+0=0( since b=0)

-5-a=0

-a=5

a=-5

therefore,a=-5 and b =0

Answer 2

Given :-

• f(x) = 2x³ - 3x² + ax + b

• Zeroes of the given polynomial are 0 and -1

To Find :-

• Value of a and b

Solution :-

To find the value of a and b, we need to put x = 0, -1 in the given polynomial.

Given that,

x = 0

x = -1

___________________________________________

Now, put x = 0 in the given polynomial

⟼2x³ - 3x² + ax + b = 0

⟼ 2×0 - 3×0² +a×0 + b = 0

⟼0 -0 +0 + b = 0

⟼ b = 0

Therefore, value of b is = 0

Again,

___________________________________________

Put the value of x = -1 and b =0 in the given polynomial

⟼ 2x³ - 3x² + ax + b = 0

⟼ 2×(-1)³ -3 ×(-1)² + a×(-1) + b = 0

⟼ 2× (-1) -3 ×1 -a +0 = 0

⟼ -2 -3 - a = 0

$⟼ a = - 5$

Hence, the value of a and b are -5 and 0 respectively.