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Ask QuestionPosted by Nisha Yash 5 years, 6 months ago
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Posted by Kashish Nagar 5 years, 6 months ago
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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.
Posted by Vishakha Yadav 5 years, 6 months ago
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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..
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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.
Posted by Gm Sir Appujeeth 5 years, 6 months ago
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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
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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.
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