Question

If x2 – 8x + p and x2 – 11x + 4p have a common factor, then the values of p is equal to
1. 1, 3
2. 0, 7
3. 0, 3
4. 5, 3
PLS REPLY FAST

Answer 1

Answer:

option (2)

Step-by-step explanation:

Given polynomials are

f(x) = x2 – 8x + p and p(x) = x2 – 11x + 4p

Let 'a' is the common factor of x2 – 8x + p and x2 – 11x + 4p

=> f(a) = p(a)

=> a² – 8(a) + p = a² – 11(a) + 4p

=> 11a – 8a = 4p - p

=> 3a = 3p => a = p

substituting in f(a) = 0 or p(a) = 0

a² - 8a + p = 0 => p² - 8p + p = 0

=> p² - 7p = 0

=> p (p - 7) = 0

=> p = 0 or p - 7 = 0

.•. p = 0 or p = 7