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4 years ago

Factor the expression completely.

Mathematics

1 answer:

navik [9.2K]4 years ago

4 0

Answer:

(2n + 7) (2n +7)

Step-by-step explanation:

To solve this problem we need to factorize 4n^2 + 28n +49 as shown below

$4n^2 + 28n +49\\=>4n^2 + 14n + 14n +49\\=>2n(2n + 7) + 7(2n +7)\\=> (2n + 7) (2n +7)$

thus, after factorization we see that first option is correct one

(2n + 7) (2n +7)

we can validate this by expanding it

2n (2n +7) + 7 (2n+7)\

=> 4n^2 + 14n + 14n + 49 = 4n^2 + 28n +49 (which is equal to the problem stated expression)

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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

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Step-by-step explanation:

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3 years ago

What is the constant rate of change shown in the graph

podryga [215]

I would say C instead of A but I am not so sure.

4 0

3 years ago

Read 2 more answers

Add using scientific notation. (5.2 x 10') + (3.01 x 10^)

satela [25.4K]

Answer: What's the exponents?

Step-by-step explanation:

5.2+3.01=8.21

but then there's no exponents that you stated. So it would be 8.21x10^?

If the tens do have exponents above them, add them together.

I hope this answer helps you!

7 0

4 years ago

(13 POINTS AND BRAINLIEST FOR BEST)

nordsb [41]

<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ Simply multiply 7.25 by 200:

7.25 x 200 = 1450

The actual tower is 1450 feet

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

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3 years ago