Question

find the value of k, if x - 1 is a factor of p(x) in each of the following cases (1) p(x) = kx square - √2x + 1

Answer 1

p(x) = kx² - √2x + 1

Now x - 1 is a factor
x - 1 = 0
x = 1

Now put x = 1 in p(x)
p(1) = 0
p(1) = k(1)² - √2(1) + 1 = 0
k - √2 + 1 = 0
k = √2 - 1

So required value of k = √2 - 1

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