Math, asked by fjzgdidtiyiftus, 4 months ago

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 – 3x + 7
(ii) y2 + √2
(iii) 3 √t + t√2
(iv) y+ \{ 2 }{ y }
(v) x10+ y3+t50

Give a proper answer.​

Answers

Answered by Anonymous
14

 \huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}

(i) We have 4x2 – 3x + 7 = 4x2 – 3x + 7x0

It is a polynomial in one variable i.e., x

because each exponent of x is a whole number.

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(ii) We have y2 + √2 = y2 + √2y0

It is a polynomial in one variable i.e., y

because each exponent of y is a whole number.

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(iii) We have 3 √t + t√2 = 3 √t ½ + √2.t

It is not a polynomial, because one of the exponents of t is \frac { 1 }{ 2 },

which is not a whole number.

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(iv) We have y + y+\sf\frac { 2 }{ y } = y + 2.y-1

It is not a polynomial, because one of the exponents of y is -1,

which is not a whole number.

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(v) We have x10+ y3 + t50

Here, exponent of every variable is a whole number, but x10 + y3 + t50 is a polynomial in x, y and t, i.e., in three variables.

So, it is not a polynomial in one variable.

{\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}

Answered by VinCus
39

\rule{220}{3}

{\huge{\underline{\underline{\frak{\red{Required\:answer: }}}}}}

--i) 4x²- 3x+7

The given expression has single variable x.

The exponent of x is whole number i.e, 2.

Hence, The given expression is a

polynomial in one variable..

\rule{220}{3}

--ii) y²+√2

The exponent of y is a whole number i.e , 2.

Hence, the given expression is a

polynomial in one variable..

\rule{220}{3}

--iii) 3√t + t√2

Here the exponent of the first term is 2, which is not a whole number.

Therefore, its not a polynomial.

\rule{220}{3}

--iv) y + 2/y

y + 2y-¹

Here the exponent of the second term is negative (-1), which is not a whole number.

Hence, the given expression is not a

polynomial.

\rule{220}{3}

--》v) x¹⁰ + y³+ t⁵⁰

The expression has three variables x, y, t.

Hence, it is not a polynomial in one

variable.

\rule{220}{3}

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