Question

find the value if x-a is afactor of x^3-ax^2+2x+a-5​

Answer 1

Answer:

⇒ (x−a) is factor of x

3

−ax

2

+2x+a−1

⇒ Then, a is the zero of polynomial p(x)=x

3

−ax

2

+2x+a−1

⇒ p(x)=x

3

−ax

2

+2x+a−1

⇒ p(a)=(a)

3

−a(a)

2

+2(a)+a−1

⇒ 0=a

3

−a

3

+2a+a−1

⇒ a

3

−a

3

+2a+a−1=0

⇒ 3a−1=0

⇒ 3a=1

∴ a=

3

1

Answer 2

Answer:

$a = \frac{5}{3}$

Step-by-step explanation:

if x-a is factor of equation, then x=a, will satisfy the eqn

${x}^{3} - a {x}^{2} + 2x + a - 5 = 0 \\ put \: x = a \\ {a}^{3} - a( {a}^{2} ) + 2a +a - 5 = 0 \\ {a}^{3} - {a}^{3} + 3a - 5 = 0 \\ 3a - 5 = 0 \\ a = \frac{5}{3}$