State why the following algebraic expressions are not polynomials -a- 2x2 - 3 under root x - 5b- 1- x2 - 2x - 5c- 2x3 - 3-x - 4

nbsp;Let nbsp;x nbsp;be nbsp;a nbsp;variable, nbsp;n nbsp;be nbsp;a nbsp;positive nbsp;integer nbsp;and nbsp;a0, nbsp;a1, nbsp;a2,. ...

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Standard X

Mathematics

Polynomial

State why the...

Question

State why the following algebraic expressions are not polynomials :
a) 2x² - 3 under root x + 5
b) 1/ x² - 2x + 5
c) 2x³ - 3/x + 4

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Solution

$Let x be a variable, n be a positive integer and a_{0}, a_{1}, a_{2}, . . . . . . a_{n} be the constants (real numbers) . Then, a_{n} x^{n} + a_{n - 1} x^{n - 1} + . . . . . . . . . + a_{1} x + a_{0} is known as the polynomial in variable x . (1) . 2 x^{2} - 3 \sqrt{x} + 5 = 2 x^{2} - 3 x^{1 / 2} + 5 The above expression is not a polynomial as the exponent of x in - 3 x^{1 / 2} is not a positive integer . (2) . \frac{1}{x^{2}} - 2 x + 5 = x^{- 2} - 2 x + 5 The above expression is not a polynomial as the exponent of x in x^{- 2} is not a positive integer . (3) . 2 x^{3} - \frac{3}{x} + 4 = 2 x^{3} - 3 x^{- 1} + 4 The above expression is not a polynomial as the exponent of x in - 3 x^{- 1} is not a positive integer .$

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Similar questions

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^{5} - 2 x^{3} + x + \sqrt{3}$

(ii) $y^{3} + \sqrt{3} y$

(iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$

(iv) $x^{1000} - 1$

(v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$

(vi) $x^{- 2} + 2 x^{- 1} + 3$

(vii) $1$

(viii) $\frac{- 3}{5}$

(ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$

(x) $\sqrt[2]{2} x^{2} - 8$

(xi) $\frac{1}{2 x^{2}}$

(xii) $\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$

(xiii) $\frac{3}{5} x^{2} - \frac{7}{3} x + 9$

(xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$

(xv) $2 x^{3} + 3 x^{2} + \sqrt{x} - 1$

Which of the following is not a polynomial ?

(a) $\sqrt{3} x^{2} - 2 \sqrt{3} x + 5$ (b) $9 x^{2} - 4 x + \sqrt{2}$

Q. Taking x = 4, find the values of the following algebraic expressions.

(1) 5 − x
(2) 3 (5 − x)
(3) (5 − x)²
(4) (x + 2)²
(5) 3(x + 2)
(6) 2 (x + 2) + 3

Which of the following expressions are polynomials?
(i) $x^{2} + 4 + y^{3}$
(ii) $4 - x^{- 1} + z^{3}$
(iii) $2 x^{2} - \frac{2}{x}$

Which of the following is not a quadratic equation?
(a) $3 x - x^{2} = x^{2} + 5$
(b) $(x + 2)^{2} = 2 (x^{2} - 5)$
(c) $(2 x + 3)^{2} = 2 x^{2} + 6$
(d) $(x - 1)^{2} = 3 x^{2} + x - 2$

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State why the following algebraic expressions are not polynomials :a) 2x2 - 3 under root x + 5b) 1/ x2 - 2x + 5c) 2x3 - 3/x + 4

State why the following algebraic expressions are not polynomials :
a) 2x² - 3 under root x + 5
b) 1/ x² - 2x + 5
c) 2x³ - 3/x + 4