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339 questions tagged with definition-polynomial.
Which is the correct identification of (p(x)=5x-2)?
A. द्विघात एकपदीQuadratic monomial
\(5x^2\) में एक पद है और घात (2) है। इसलिए यह द्विघात एकपदी है। / \(5x^2\) has one term and degree (2). Therefore, it is a quadratic monomial.
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Which polynomial has no \(x^2\) term but has degree (4)?
A. \(x^4+3x-2\)
\(x^4+3x-2\) में \(x^2\) पद नहीं है पर सबसे बड़ी घात (4) है। गायब पद घात को नहीं रोकता। / In \(x^4+3x-2\), the \(x^2\) term is missing but the highest power is (4). A missing term does not affect validity.
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Which expression is a polynomial in (x) with a decimal coefficient?
A. \(1.5x^2-4x+3\)
दशमलव (1.5) वास्तविक गुणांक है। (x) की घातें (2), (1) और (0) मान्य हैं। / The decimal (1.5) is a real coefficient. The powers of (x) are (2), (1), and (0), which are valid.
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Why is \(x^2+x^{-1}+1\) not a polynomial?
B. क्योंकि \(x^{-1}\) की घात ऋणात्मक हैBecause the power in \(x^{-1}\) is negative
\(x^{-1}\) की घात ऋणात्मक है। बहुपद में ऐसी घात स्वीकार्य नहीं होती। / The power in \(x^{-1}\) is negative. Such a power is not allowed in a polynomial.
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Which statement is false for a polynomial?
C. चर हर में रह सकता हैThe variable can be in the denominator
यदि चर हर में आता है तो अक्सर उसकी घात ऋणात्मक हो जाती है। बहुपद में ऋणात्मक घात मान्य नहीं होती। / If the variable appears in the denominator, its power often becomes negative. Negative powers are not valid in a polynomial.
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Which expression is a polynomial of degree (6)?
C. \(2x^6-x^3+8\)
\(2x^6-x^3+8\) में सभी घातें मान्य हैं और सबसे बड़ी घात (6) है। इसलिए इसकी घात (6) है। / In \(2x^6-x^3+8\), all powers are valid and the highest power is (6). So its degree is (6).
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Which powers are present in \(2x^5+x^2-3\)?
A. (5), (2), (0)
\(2x^5\) की घात (5), \(x^2\) की घात (2), और स्थिर पद की घात (0) मानी जाती है। / The power of \(2x^5\) is (5), the power of \(x^2\) is (2), and the constant term is treated as power (0).
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What are the degree and type of (p(u)=3u-2-4u+10)?
B. घात (2), द्विघातDegree (2), quadratic
सबसे बड़ी घात (2) है। इसलिए यह द्विघात बहुपद है। / The highest power is (2). Therefore, it is a quadratic polynomial.
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Which expression has a negative constant term and is still a polynomial?
A. \(x^2-11\)
ऋणात्मक स्थिर पद होने से व्यंजक बहुपद बनने से नहीं रुकता। \(x^2-11\) में सभी घातें मान्य हैं। / A negative constant term does not prevent an expression from being a polynomial. In \(x^2-11\), all powers are valid.
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Which expression is not a polynomial in (x) but has real coefficients?
B. \(\frac{4}{x}-3\)
वास्तविक गुणांक होना पर्याप्त नहीं है। \(\frac{4}{x}\) में (x) की घात (-1) है इसलिए यह बहुपद नहीं है। / Having real coefficients is not enough. In \(\frac{4}{x}\), the power of (x) is (-1), so it is not a polynomial.
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What is the degree of \(x^3+2x^2+x+5\)?
D. (3)
सबसे बड़ी घात \(x^3\) में (3) है। इसलिए बहुपद की घात (3) है। / The highest power is (3) in \(x^3\). Therefore, the degree of the polynomial is (3).
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Which option gives the main condition of a polynomial correctly?
B. चर की घातें शून्य या धनात्मक पूर्णांक होनी चाहिएVariable powers must be zero or positive integers
बहुपद में चर की घातें शून्य या धनात्मक पूर्णांक होती हैं। यह परिभाषा की सबसे महत्वपूर्ण शर्त है। / In a polynomial, powers of the variable are zero or positive integers. This is the most important condition in the definition.
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If (a=0) in (p(x)=ax-4+3x-2-1), what will be the degree?
C. (2)
(a=0) होने पर \(x^4\) वाला पद हट जाता है। शेष बहुपद \(3x^2-1\) की घात (2) है। / When (a=0), the \(x^4\) term disappears. The remaining polynomial \(3x^2-1\) has degree (2).
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Which expression is a polynomial in (m)?
C. \(2m^5-3m+1\)
\(2m^5-3m+1\) में (m) की घातें (5), (1) और (0) हैं। ये सभी मान्य हैं। / In \(2m^5-3m+1\), the powers of (m) are (5), (1), and (0). All are valid.
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Which expression is a polynomial but does not have degree (1)?
B. \(x^2+6\)
\(x^2+6\) बहुपद है और इसकी घात (2) है। इसलिए इसकी घात (1) नहीं है। / \(x^2+6\) is a polynomial and its degree is (2). Therefore, its degree is not (1).
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In which expression does \(x^0\) form a constant term?
A. \(6x^0+5x\)
\(x^0=1\) माना जाता है जब \(x\neq0\)। इसलिए \(6x^0\) स्थिर पद (6) जैसा है। / \(x^0=1\) when \(x\neq0\). So \(6x^0\) behaves like the constant term (6).
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Which statement is correct about \(4x^2+\frac{3}{4}x-9\)?
B. यह बहुपद है क्योंकि चर की घातें मान्य हैंIt is a polynomial because variable powers are valid
भिन्न गुणांक बहुपद में मान्य होते हैं। यहाँ (x) की घातें (2), (1) और (0) हैं। / Fractional coefficients are allowed in polynomials. Here the powers of (x) are (2), (1), and (0).
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Which expression is a polynomial with no linear (x)-term?
A. \(x^4+3x^2-5\)
बहुपद में हर घात का पद होना जरूरी नहीं है। \(x^4+3x^2-5\) में सभी उपस्थित घातें मान्य हैं। / A polynomial need not have every power term. In \(x^4+3x^2-5\), all present powers are valid.
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Which is the correct identification of (p(x)=x-2-4x+4)?
B. द्विघात त्रिपदीQuadratic trinomial
इसकी घात (2) है और इसमें (3) पद हैं। इसलिए यह द्विघात त्रिपदी है। / Its degree is (2) and it has (3) terms. Therefore, it is a quadratic trinomial.
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How many terms are there in \(5x^3-2x^2+9x-6\)?
C. (4)
इसमें \(5x^3\), \(-2x^2\), (9x) और (-6) चार पद हैं। पदों को चिन्ह सहित गिनें। / It has four terms: \(5x^3\), \(-2x^2\), (9x), and (-6). Count terms with their signs.
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Which expression is a polynomial in (x) if (k) is treated as a constant?
A. \(kx^3-2x+8\)
(k) स्थिर की तरह गुणांक है। (x) की घातें (3), (1) और (0) हैं इसलिए यह बहुपद है। / (k) acts like a constant coefficient. The powers of (x) are (3), (1), and (0), so it is a polynomial.
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Why is \(x^2+2x^{3/2}+5\) not a polynomial?
D. क्योंकि (x^{32}) की घात पूर्णांक नहीं है / Because the power in \(x^{3 / 2}\) is not an integer
बहुपद में चर की घातें पूर्णांक होनी चाहिए। \(x^{3/2}\) में घात \(\frac{3}{2}\) है। / In a polynomial, powers of the variable must be integers. In \(x^{3/2}\), the power is \(\frac{3}{2}\).
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Which option correctly shows a polynomial in (x) and its degree?
A. \(x^4+x\), घात (4)\(x^4+x\), degree (4)
\(x^4+x\) में घातें (4) और (1) हैं। यह बहुपद है और इसकी घात (4) है। / In \(x^4+x\), the powers are (4) and (1). It is a polynomial and its degree is (4).
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What is the degree of (7) as a polynomial?
D. (0)
(7) शून्य से अलग स्थिर बहुपद है। ऐसे बहुपद की घात (0) होती है। / (7) is a non-zero constant polynomial. Such a polynomial has degree (0).
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If (p(x)=6x-4+0x-6-3x-2+5), what is the degree of (p(x))?
B. (4)
\(0x^6\) शून्य पद है इसलिए घात तय नहीं करता। सबसे बड़ी अशून्य घात (4) है। / \(0x^6\) is a zero term, so it does not determine the degree. The highest non-zero power is (4).
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Which expression is a linear polynomial in (z)?
D. (8z-3)
रैखिक बहुपद की घात (1) होती है। (8z-3) में सबसे बड़ी घात (1) है। / A linear polynomial has degree (1). In (8z-3), the highest power is (1).
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Which is the correct identification of \(2x^3-5x+4\)?
C. घन त्रिपदी बहुपदCubic trinomial polynomial
इसकी सबसे बड़ी घात (3) है और इसमें (3) पद हैं। इसलिए यह घन त्रिपदी बहुपद है। / Its highest power is (3) and it has (3) terms. Therefore, it is a cubic trinomial polynomial.
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Which statement is correct about \(3y^2+\sqrt{5}y-8\)?
D. यह (y) में बहुपद हैIt is a polynomial in (y)
\(\sqrt{5}\) केवल वास्तविक गुणांक है और मान्य है। (y) की घातें (2), (1) और (0) हैं। / \(\sqrt{5}\) is only a real coefficient and is allowed. The powers of (y) are (2), (1), and (0).
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What is the degree of the polynomial \(9t^5-4t^3+2t-1\)?
C. (5)
बहुपद की घात सबसे बड़ी चर-घात होती है। यहाँ सबसे बड़ी घात (5) है। / The degree of a polynomial is the highest power of the variable. Here the highest power is (5).
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If (a=0) in (p(x)=ax-3+2x-1), what will be the degree of the polynomial?
C. (1)
(a=0) रखने पर \(x^3\) वाला पद हट जाता है। शेष बहुपद (2x-1) की घात (1) है। / When (a=0), the \(x^3\) term disappears. The remaining polynomial (2x-1) has degree (1).
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