JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(S=\{x^{3}+ax^{2}+bx+c:a, b, c\in N\) and \(a, b, c\le 20\}\) be a set of polynomials. Then the number of polynomials in S, which are divisible by \(x^{2}+2,\) is
- A 20
- B 6
- C 120
- D 10
Answer & Solution
Correct Answer
(D) 10
Step-by-step Solution
Detailed explanation
\(x^{3}+ax^{2}+bx+c=(x^{2}+2)(x+\frac{c}{2})\) \(x^{2}:a=\frac{c}{2}\) \(x:b=2\) \(b=2, a=\frac{c}{2}, c\in\{2,4,...,20\}\) Number of polynomials in 'S' will be 10.
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