Home
Class 14
MATHS
When (x-a) is a factor of (x^3-3x^2a+2a^...

When (x-a) is a factor of `(x^3-3x^2a+2a^2x+p)` then find the value of p is:

A

0

B

1

C

2

D

3

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the value of \( p \) such that \( (x - a) \) is a factor of the polynomial \( x^3 - 3x^2a + 2a^2x + p \). We can use the Factor Theorem, which states that if \( (x - a) \) is a factor of a polynomial \( f(x) \), then \( f(a) = 0 \). ### Step-by-step Solution: 1. **Define the polynomial**: Let \( f(x) = x^3 - 3x^2a + 2a^2x + p \). 2. **Apply the Factor Theorem**: Since \( (x - a) \) is a factor, we have: \[ f(a) = 0 \] 3. **Substitute \( a \) into the polynomial**: We calculate \( f(a) \): \[ f(a) = a^3 - 3a^2a + 2a^2a + p \] 4. **Simplify the expression**: Simplifying \( f(a) \): \[ f(a) = a^3 - 3a^3 + 2a^3 + p \] Combine like terms: \[ f(a) = (1 - 3 + 2)a^3 + p = 0 \] This simplifies to: \[ 0a^3 + p = 0 \] 5. **Solve for \( p \)**: From the equation \( 0 + p = 0 \), we find: \[ p = 0 \] ### Conclusion: Thus, the value of \( p \) is \( 0 \).
Promotional Banner

Topper's Solved these Questions

  • CO-ORDINATE GEOMETRY

    QUANTUM CAT|Exercise QUESTION BANK|72 Videos

  • FUNCTIONS AND GRAPHS

    QUANTUM CAT|Exercise QUESTION BANK|286 Videos

Similar Questions

Explore conceptually related problems

If x^(2)+2x-5 is a factor of x^(4)-2x^(3)+px^(2) +qx-35 , then find the value of p^(2)-q .

If (x + 6) is a factor of f (x) = x ^(3) + 3x ^(2) + 4x + P, then find the value of P.

If x+2a is factor of x^(5)-4a^(2)x^(3)+2x+2a +3 , then find the value of a .

If (x-3) is a factor of p(x)=x^(3)-mx^(2)+(m+1)x-12 find the value of 'm'

For a polynomial p(x) of degree ge1, p(a)=0 , where a is a real number, then (x-a) is a factor of the polynomial p(x) Find the value of k if x-1 is a factor of 4x^(3)+3x^(2)-4x+k .

If p(x)=2+x+2x^(2)-x^(3) then find the value of p(sqrt(2))

If (x^(2)-3x+2) is a factor of x^(4)-px^(2)+q=0, then the values of p and q are

if (x+1) and (x-1) are factors of p(x)=ax^(3)+x^(2)-2x+b find the values of a&b