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Addition and Subtraction of a Matrix

30. Let a,b,c...

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30. Let a,b,c and k be real numbers and p(x) be the polynomial (x-a) (x-b) (x-c) + x. If p(k)=k ,then the sum of all possible values of k is what?

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The value of k for which the polynomial $x^{3} + 10 x^{2} + k x + 1$ is continuous for all values of x is

f (x) = x^{5} + a x^{4} + b x^{3} + c x^{2} + d x - 420

a, b, c, d

are real parameters, be a polynomial. If all zeros of the polynomial

f (x)

are integers larger than

1,

f (4)

k,

k

is divisible by

| l n | x | | = | k - 1 | - 4

has exactly two distinct real roots for

x \in R - {0}

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Q. The roots of

(x - a) (x - c) + k (x - b) (x - d) = 0

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