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3 years ago

Plz help me!! Will give brainliest to who ever gets it right! Thanks

Mathematics

2 answers:

GarryVolchara [31]3 years ago

6 0

Answer:

5. 57 9. 63

Step-by-step explanation:

Im Smart

likoan [24]3 years ago

5 0

Answer:

4 and 5 the answer choices are wrong. 6.=150 9.=63. 10.=vertical. i dont have the chart for 8

Step-by-step explanation:

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Evaluate n^2 -m. If you n=-5 and m=3

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Answer:

Step-by-step explanation:

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Please answer this question

Tems11 [23]

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

<h3>Given :- </h3>

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

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

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

Here, we have polynomial

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

We know that, 

Sum of the zeroes of the quadratic polynomial

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

And 

Product of zeroes

$\sf{ {\alpha}{\beta} = {\dfrac{c}{a}}}$

Now, we have to find the polynomials having zeroes :-

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

Therefore ,

Sum of the zeroes

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

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

$\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{{\alpha}+{\beta}}{{\alpha}{\beta}}}}$

$\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{-b/a}{c/a}}}$

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

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

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

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 .

We know that, 

For any quadratic equation

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

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

Hence, The polynomial is x² + (-bc-ab/c)x + c/a + a/c + 2 .

<h3>Some basic information :-</h3>

• Polynomial is algebraic expression which contains coffiecients are variables.

• 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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2 years ago