Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleEasy2 minQB

MathematicsEasyinteger

The number of polynomials of the form $x^{3} + a x^{2} + b x + c$ which are divisible by $x^{2} + 1$ where $a, b, c \in {1, 2, 3, \dots, 10}$ is 10 K , then K is $____$ .

Answer:

Solution:

$x^{2} + 1 = (x + i) (x - i)$

$b = 1, a = c$

No.of ways of choosing $a, b, c = 10 = 10 \times 1$

$∴ K = 1$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Fundamental Principle

⏱ 2mℹ️ Source: QB

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