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बहुपद

Question
CBSEHHIMAH10009885
Wired Faculty App

3x4 + 6x3 – 2x2 - 10x - 5 के अन्य सभी शून्यक ज्ञात कीजिए, यदि इसके दो शून्यक

square root of 5 over 3 end root space और space minus space square root of 5 over 3 end root हैंl

Solution

दिया है: straight p left parenthesis straight x right parenthesis space equals space 3 straight x to the power of 4 space plus space 6 straight x cubed space minus space 2 straight x squared space minus space 10 straight x space minus space 5 और straight alpha space equals space square root of 5 over 3 end root comma space space space space straight beta space equals space minus space square root of 5 over 3 end root
∵      दो शून्यक है square root of 5 over 3 end root space और space minus space square root of 5 over 3 end root
open parentheses space straight x space minus space square root of 5 over 3 end root space close parentheses space open parentheses space straight x space plus space square root of 5 over 3 end root space close parentheses space equals space open parentheses space straight x squared space minus space 5 over 3 space close parentheses दिए हुए बहुपद p(x) का एक गुणनखंड हैl

3 straight x to the power of 4 space plus space 6 straight x cubed space minus space 2 straight x squared space minus space 10 straight x space minus space 5 space equals space open parentheses space straight x squared space minus space 5 over 3 space close parentheses left parenthesis space 3 straight x squared space plus 6 straight x space plus space 3 space right parenthesis space plus space 0 space equals space open parentheses space straight x squared space minus space 5 over 3 space close parentheses left curly bracket space 3 straight x squared space plus space 3 straight x space plus space 3 straight x space plus space 3 space right curly bracket space equals space open parentheses space straight x squared space minus space 5 over 3 space close parentheses left curly bracket space 3 straight x space left parenthesis space straight x space plus space 1 space right parenthesis space plus space 3 space left parenthesis space straight x space plus space 1 space right parenthesis space equals space open parentheses straight x squared space minus space 5 over 3 space close parentheses left parenthesis space 3 straight x space plus space 3 space right parenthesis left parenthesis space straight x space plus space 1 space right parenthesis
( 3x + 3 )( x + 1 ) = 3 ( x + 1 )( x + 1)
शून्यक: x = -1, -1
अत दिए हुए चतुर्थ घात बहुपद के शून्यक हैं:
square root of 5 over 3 end root comma space minus space square root of 5 over 3 end root comma space minus space 1 comma space minus space 1

Some More Questions From बहुपद Chapter

विभाजन एल्गोरिथ्म का प्रयोग करके निम्न में से p(x) को g(x) से भाग देने पर भागफल और शेषफल ज्ञात कीजिए:
p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2

विभाजन एल्गोरिथ्म का प्रयोग करके निम्न में से p(x) को g(x) से भाग देने पर भागफल और शेषफल ज्ञात कीजिए:

p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x

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