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  • 1 answers

Gaurav Seth 5 years, 6 months ago

P(X) = 4✓3X²+5X-2✓3

=> 4✓3X² +8X-3X-2✓3


=> 4X(✓3X+2) -✓3(✓3X+2)


=> (✓3X+2)(4X-✓3) = 0


=> (✓3X +2)= 0 OR (4X-✓3) = 0


=> X = -2/✓3 OR X = ✓3/4


-2/✓3 and ✓3/4 are the two zeros of the given polynomial.


Let Alpha = -2/✓3 and beta = ✓3/4


Relationship between the zeros and Coefficient.


Sum of zeros = (Alpha + Beta) = -2/✓3 + ✓3/4 = -8+3/4✓3 = -5/4✓3 = - ( Coefficient of X/Coefficient of X²)


And,


Product of zeros = (Alpha × Beta) = -2/✓3 × ✓3/4 = -2✓3/4✓3 = Constant term/Coefficient of X².

 

  • 1 answers

Gaurav Seth 5 years, 6 months ago

Let √2 be a rational number 

Therefore, √2= p/q  [ p and q are in their least terms i.e., HCF of (p,q)=1 and q ≠ 0

On squaring both sides, we get 
                   p²= 2q²                                                                                    ...(1)
Clearly, 2 is a factor of 2q²
⇒ 2 is a factor of p²                                                                    [since, 2q²=p²]
⇒ 2 is a factor of p

 Let p =2 m for all m ( where  m is a positive integer)

Squaring both sides, we get 
            p²= 4 m²                                                                                          ...(2)
From (1) and (2), we get 
           2q² = 4m²      ⇒      q²= 2m²
Clearly, 2 is a factor of 2m²
⇒       2 is a factor of q²                                                      [since, q² = 2m²]
⇒       2 is a factor of q 

Thus, we see that both p and q have common factor 2 which is a contradiction that H.C.F. of (p,q)= 1

     Therefore, Our supposition is wrong

Hence √2 is not a rational number i.e., irrational number..

  • 1 answers

Mansi Mishra 5 years, 6 months ago

I think u say that polynmial. Polynomials is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s
1. If the zeroes of the quadratic polynomial ?2+(?+1)?+? are 2 and –3, then find the value of ? ,?. 2. If one zero of the polynomial (?2+9)?2+13?+6? is reciprocal of the other, find the value of ?. 3. If ? and ? are the zeroes of the polynomial 2?2+5?+? such that ?2+?2+??=214, then find the value of ?. 4. If ? and ? are the zeroes of the polynomial ?2−?(?+1)−?, then prove that (?+1)(?+1)=1−? 5. If ? and ? are the zeroes of the polynomial ?2+??+?, then find the polynomial whose zeroes are 1? and 1? . 6. If a polynomial ?(?)=?3−7?+? when divided by (?−1) leaves remainder 2, then find the value of ?. 7. If the polynomial (?4+2?3+8?2+12?+18) is divided by another polynomial (?2+5), the remainder comes out to be (??+?). Find the values of ? and ?. 8. Find a quadratic polynomial whose sum and product of zeroes are respectively −32√5 and −12. Also, find the zeroes of the polynomial so obtained. 9. Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials: 2?2−(1+2√2)?+√2 10. If the remainder on division of ?3+2?2+??+3 by x – 3 is 21, find the quotient and the value of k. Hence, find the zeroes of the cubic polynomial ?2+2?2+??−18. 11. If two zeroes of the polynomial ?(?)=?4−6?3−26?2+138?−35 are (2+√3) and (2−√3), find the other zeroes.
  • 1 answers

Mansi Mishra 5 years, 6 months ago

Ye question karne ke bajaye do answer yaad ho jayaga kaha se late ho question. ??????
  • 1 answers

Rohan Singh 5 years, 6 months ago

25
  • 2 answers

Yogita Ingle 5 years, 6 months ago

Trigonometry is a branch of mathematics dealing with relations involving lengths and angles of triangles. It can, in a simpler manner, be called the study of triangles. The angles are either measured in degrees or radians.

Aditi Jain 5 years, 6 months ago

Trigonometry means "triangle measurement"
  • 1 answers

Yogita Ingle 5 years, 6 months ago

2x + 3 = 5/3

2x = 5/3 - 3

2x = (5-9)/3

2x = -4/3

x = -4/6

  • 1 answers

Archana Singh 5 years, 6 months ago

Y=5,x=-2
  • 2 answers

Neha Kakkar ?? 5 years, 6 months ago

Yes,

Aawesh Khan 5 years, 6 months ago

Yes
  • 5 answers

Kyōka ( Demon Snow ) 5 years, 6 months ago

Thank you Archana Singh ??

Archana Singh 5 years, 6 months ago

Alpha+beta+gamma=-b/a Alpha×beta×gamma=-d/a Alpha×beta+beta×gamma+gamma×alpha=c/a

Kyōka ( Demon Snow ) 5 years, 6 months ago

PLEASE somebody answer me correctly.

Kyōka ( Demon Snow ) 5 years, 6 months ago

No it is not possible for all cubic polynomials. ???

Aawesh Khan 5 years, 6 months ago

1
  • 1 answers

Archana Singh 5 years, 6 months ago

Sin(A+B)=underoot3/2 Sin(A+B)=Sin 60 A+B=60 Similarly (A-B)=30 Substituting B=15,A=45
  • 2 answers

Kyōka ( Demon Snow ) 5 years, 6 months ago

Let √2 = x. Now 3x - x = 2x. Therefore answer = 2√2.
2√2...
  • 1 answers

Varshini Rm 5 years, 6 months ago

Discriminate=b^2-4ac =(5)^2-4*2*3 =25-24 1
  • 0 answers
  • 2 answers

Miss__ Thakur 5 years, 6 months ago

IRRATIONAL NUMBER..

Yogita Ingle 5 years, 6 months ago

  • The sum of two irrational numbers is always an irrational number.
  • The difference of two distinct irrational numbers is always an irrational number.
  • 0 answers
  • 4 answers

Neha Kakkar ?? 5 years, 6 months ago

Highest Common Factor

Kyōka ( Demon Snow ) 5 years, 6 months ago

Highest common factor.
Highest common factor..

Paramjeet Kaur 5 years, 6 months ago

Highest common factor
  • 1 answers

Yogita Ingle 5 years, 6 months ago

  • 0 answers
  • 1 answers

Mansi Mishra 5 years, 6 months ago

Similarity is a quality of scaling: two shapes are similar if you can scale one to be like the other, like these triangles ABC and DEF. Since all circles are of the same shape (they only vary by size), any circle can be scaled to form any other circle. Thus, all circles are similar!
  • 1 answers

Syed Anas Ali 5 years, 6 months ago

12 ×÷
  • 0 answers

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