Question

If x=2and x=0 are root of the polynomial f(x)=2x^3-3x^2+ax+b,then find the value of a and b

Answer 1

Given :

• The given Polynomial is 2x³ - 3x² + ax + b and 2, 0 are it's zeroes.

To Find :

• The value of a & b.

Let us substitute x = 2 in the given equation.

⟶ $\sf{ 2 {x}^{3} - 3 {x}^{2} - ax + b = 0}$

⟶ $\sf{2 {(2)}^{3} - 3{(2)}^{2} + 2a + b = 0}$

⟶ $\sf{16 - 12 + 2a + b = 0}$

⟶ $\sf{4 + 2a + b = 0}$

⟶ $\sf{2a + b = - 4}$

⟶ $\sf{a + b = - 2}$

⟶ $\sf{ \red{a = - 2 - b}}....(1)$

Let us substitute x = 0 in the given equation as it is given that 0 is one pf the root of the Equation. Also, Let's substitute Let's substitute (1) in the Equation.

Now,

⟶ $\sf{2 {(0)}^{ 3} - 2 {(0)}^{2} + 2(0) + b = 0}$

⟶ $\boxed{\sf{ \blue{b = 0}}}$

Let us substitute the value of b in (1), we get :

⟶ $\sf{a = - 2 - 0}$

⟶ $\boxed{ \sf{ \blue{a = - 2}}}$