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spayn [35]
3 years ago
10

Write a polynomial function with the zeros 1, -2i

Mathematics
1 answer:
Helga [31]3 years ago
7 0
F( x ) = ( x - 1 ) ( x + 2i )( x - 2i ), because the zeroes are 1, -2i, +2i ;
f( x ) = ( x - 1 )( x^2 - 4i^2 ) = ( x - 1 )( x^2 + 4 ) = x^3  - x^2 + 4x - 4 ;
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Rationalize the denominator:<br><br> GRADE 9<br><br><br> CBSE
kakasveta [241]

Answer:

1. a)

\begin{gathered} \frac{2}{ \sqrt{3} - 1 } = \frac{2}{ \sqrt{3} - 1} \times \ \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1 } \\ = \frac{2 \sqrt{3} + 2 } {( \sqrt{3} ) {}^{2} - 1 {}^{2} } = \frac{2 \sqrt{} 3}{3 - 1} = \frac{2 \sqrt{3} }{2} \\ = \sqrt{3} \end{gathered}

\\

b)

\begin{gathered} = > \: \: \frac{7}{ \sqrt{12} - \sqrt{5} } \\ \\  = > \: \: \frac{7}{ \sqrt{12} - \sqrt{5} } \times \frac{ \sqrt{12} + \sqrt{5} }{ \sqrt{12} + \sqrt{5} } \\ \\  = > \: \: \frac{7( \sqrt{12} + \sqrt{5} ) }{ {( \sqrt{12}) }^{2} - {( \sqrt{5}) }^{2} } \\ \\ =  > \: \: \frac{7( \sqrt{12} + \sqrt{5}) }{12 - 5} \\ \\ => \: \: \frac{ \cancel{7}( \sqrt{12} + \sqrt{5} ) }{ \cancel{7}} \\ \\ => \: \: \sqrt{12} + \sqrt{5} \end{gathered}

7 0
2 years ago
Use the three steps to solve the problem. Joe is 10 years older than James. In 8 years, twice Joe's age will equal three times J
GarryVolchara [31]
<span>x = Joe's age  and </span><span>y = James's age 
</span><span>Joe is 10 years older than James - equation - x = y + 10 
</span><span>In 8 years twice Joe's age will equal three times James's age - equation -
2(x+8) = 3(y+8) 
</span>
<span>2(x+8) = 3(y+8) </span>
<span>2(y + 10 +8) = 3(y+8) { substitute y + 10 for x </span>
<span>2(y + 18) = 3(y + 8) </span>
<span>2y + 36 = 3y + 24 </span>
<span>12 = y </span>

<span>Joe is 22 and James is 12.</span>
7 0
3 years ago
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