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Contra-Positive

Let p and ...

Question

Let $p$ and $q$ be real numbers such that $x^{2} + p x + q \neq 0$ for every real number $x$ . if $n$ is an odd positive integer, then $X^{2} + p X + q I_{n} \neq 0_{n}$ , for all real matrices X of order $n \times n$ .

A

True

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B

False

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Solution

The correct option is A True

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I f t h e r o o t s o f t h e e q u a t i o n x^{n} - p x^{n - 1} + q x^{n - 2} . . . . . . . . . . . - (\frac{10}{n})^{n} = 0 a r e r e a l (n i s o d d p o s i t i v e i n t e g e r), t h e n t h e m i n i m u m v a l u e o f p a n d q i s a a n d b . T h e v a l u e o f a + b w h e n n = 601 i s

___ (approximately)

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Contra-Positive

Standard XII Mathematics

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