Question

1)what is the degree of the polynomial
$2x {}^{2} + 5x {}^{3} + 7$
2)what is the coefficient form of
$x {}^{3} - 1$
3)which of the following is not a surd
a)
$\sqrt{7}$
b)
$\sqrt[3]{17}$
c)
$\sqrt[3]{64}$
d)
$\sqrt{193}$
4)what is the order of the surd
$\sqrt[3]{ \sqrt{5} }$

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Answer 1

Answer:

1. 3

2. (1, 0, 0, -1 )

3. c) ³√64

4. 6

Step-by-step explanation:

1. The highest index of a variable in the given polynomial is the degree of the polynomial, therefore,

2x² + 5x³ + 7

here, the highest index of the polynomial is 3

therefore, dregree of the polynomial is 3.

2. Here the guven polynomial is

x³ - 1

It can be written as

x³+ 0.x² + 0.x - 1

therefore, coefficient of the equation above is

1, 0, 0, -1

Therefore,

The coefficient form if the given equation is

( 1, 0, 0, -1 )

3.Surds are the square roots (√) of numbers which cannot be simplified into a whole or rational number.

In short surd is an irrational root

Now in the given question the option c) is not a surd as ³√64 can be simplified and 4 is its ans which is not an irrational numbet it is an rational number.

4.

$\sqrt[ n]{a} = x$

If a is a positive rational number and nth root of a is x and if x is an irrational number then x is called a surd.

In a surd, the symbol √ is called radical sign, and n is the order of surd and a is called radicand.

Therefore, here,

³√√5

³*²√5

^6√5

Therefore, order of surd ³√√5 is 6