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
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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
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