👉 EXERCISE 2.3 CLASS 10 MATHS QUESTION 4
👉 NCERT SOLUTIONS FOR CLASS 10 MATHS CHAPTER 2 EX. 2 . 3
👉 NCERT SOLUTIONS FOR CLASS 10 MATHS CHAPTER 2 POLYNOMIALS
EX. 2 . 3 , Q . (3)
👉 NCERT SOLUTIONS FOR CLASS 10 MATHS CHAPTER 2 POLYNOMIAL
(HINDI MEDIUM )
प्रश्न - (3) 3X^4 + 6X^3 - 2X^2 -10X -5 के अन्य सभी शून्यक ज्ञात कीजिये , यदि इसके दो शून्यक
√ 5 / 3 और - √ 5 / 3 हे ?
हल : चूँकि √ 5 / 3 और - √ 5 / 3 दिए गए बहुपद के दो शून्यक हे। इसलिए इसके गुणनखंड
(X -√ 5 / 3) (X +√ 5 / 3) = (X^2 - 5/3 ) होगा।
अब , (X^2 - 5/3 ) से दिए गए बहुपद में भाग देने पर हमे एक द्विघात समीकरण मिलेगा जिससे हम शेष शून्यक ज्ञात कर लेते हे। जो निम्न प्रकार हे।
इसलिए भागफल = 3X^2 + 6X + 3
अब = 3X^2 +3X +3X + 3
= 3X (X + 1 ) + 3 (X + 1 )
= (X +1 ) (3X + 3 )
X + 1 = 0 या 3X + 3 = 0
X = -1 या 3X = -3
X = -1 या X = -3 / 3
X = -1 या X = -1
अतः दिए गए बहुपद के शेष शून्यक -1 , -1 हे।
ENGLISH TRANSLATION :
Question - (3) Find all other zeroes of 3X^4 + 6X^3 - 2X^2 -10X -5, if its two zeroes
√ 5 / 3 and - √ 5 / 3 ?
Solution : Since √5 / 3 and - √5 / 3 are two zeroes of the given polynomial. so its factors
(X -√5 / 3) (X +√5 / 3) = (X^2 - 5/3 ) will be.
Now, by dividing the given polynomial by (X^2 - 5/3 ) we will get a quadratic equation from which we can find the remaining zeroes. Which is as follows.
Hence QUOTIENT = 3X^2 + 6X + 3
Now, = 3X^2 +3X +3X + 3
= 3X (X + 1 ) + 3 (X + 1 )
= (X + ) (3X + 3 )
X + 1 = 0 or 3X + 3 = 0
X = -1 or 3X = -3
X = -1 or X = -3/3
X = -1 or X = -1
Hence the remaining zeroes of the given polynomial are -1 , -1 .