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aalyn [17]
3 years ago
9

Determine o valor das seguintes expressões.

Mathematics
1 answer:
Alisiya [41]3 years ago
6 0

a). (17º-17'-17")  =  17<span><span>º + 17'/60 + 17"/3600  =  </span>17.288055...</span><span>º

</span>17.288055...º / 4 = 4.322...º =  <em>4</em><span><em>º - 19' - 19.25"  </em><em /></span><span><== <span>a resposta</span>

b) (18º: 8 + 23º: 4 - 8º)

18</span><span>º / 8  =  2.25</span><span>º
23</span><span><span>º / 4  =  </span> 5.75</span><span>º

(2.25</span><span>º + 5.75</span><span><span>º </span>- 8º) = <em>0</em></span>  <== a resposta


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\bold{\huge{\underline{ Solution }}}

<h3><u>Given </u><u>:</u><u>-</u><u> </u></h3>

• \sf{ Polynomial :- ax^{2} + bx + c }

• The zeroes of the given polynomial are α and β .

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u><u> </u></h3>

Here, we have polynomial

\sf{ = ax^{2} + bx + c }

<u>We </u><u>know </u><u>that</u><u>, </u>

Sum of the zeroes of the quadratic polynomial

\sf{ {\alpha} + {\beta} = {\dfrac{-b}{a}}}

<u>And </u>

Product of zeroes

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<u>Now, we have to find the polynomials having zeroes </u><u>:</u><u>-</u>

\sf{ {\dfrac{{\alpha} + 1 }{{\beta}}} ,{\dfrac{{\beta} + 1 }{{\alpha}}}}

<u>T</u><u>h</u><u>erefore </u><u>,</u>

Sum of the zeroes

\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} )+( {\beta}+{\dfrac{1 }{{\alpha}}})}

\sf{ ( {\alpha} + {\beta}) + ( {\dfrac{1}{{\beta}}} +{\dfrac{1 }{{\alpha}}})}

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\sf{ {\dfrac{ -b}{a}} + {\dfrac{-b}{c}}}

\bold{{\dfrac{ -bc - ab}{ac}}}

Thus, The sum of the zeroes of the quadratic polynomial are -bc - ab/ac

<h3><u>Now</u><u>, </u></h3>

Product of zeroes

\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} ){\times}( {\beta}+{\dfrac{1 }{{\alpha}}})}

\sf{ {\alpha}{\beta} + 1 + 1 + {\dfrac{1}{{\alpha}{\beta}}}}

\sf{ {\alpha}{\beta} + 2 + {\dfrac{1}{{\alpha}{\beta}}}}

\bold{ {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}

Hence, The product of the zeroes are c/a + a/c + 2 .

<u>We </u><u>know </u><u>that</u><u>, </u>

<u>For </u><u>any </u><u>quadratic </u><u>equation</u>

\sf{ x^{2} + ( sum\: of \:zeroes )x + product\:of\: zeroes }

\bold{ x^{2} + ( {\dfrac{ -bc - ab}{ac}} )x + {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}

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• There are different types of polynomial like linear polynomial , quadratic polynomial , cubic polynomial etc.

• Quadratic polynomials are those polynomials which having highest power of degree as 2 .

• The general form of quadratic equation is ax² + bx + c.

• The quadratic equation can be solved by factorization method, quadratic formula or completing square method.

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