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tankabanditka [31]
3 years ago
11

Factor & Finding Zeros x^{2} +12x+35=0

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
8 0

Answer:

x = - 7, x = - 5

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)

The factors are + 7 and + 5, since

7 × 5 = 35 and 7 + 5 = 12, hence

x² + 12x + 35 = 0 ← in standard form

(x + 7)(x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 5 = 0 ⇒ x = - 5

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What is the factorization of the polynomial below? 2x2 + 28x + 98 A. (x + 7)(x + 2) B. (x + 7)(x + 14) C. (2x + 7)(x + 7) D. 2(x
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What is the equation when y=5x+4 is reflected over the x-axis, y-axis &amp; y=x?
tigry1 [53]

Answer:

A) y=-5x-4

B) y=-5x+4

C) y=\frac{x-4}{5}

Step-by-step explanation:

So we have the equation:

y=5x+4

Let's write this in function notation. Thus:

y=f(x)=5x+4

A)

To flip a function over the x-axis, multiply the function by -1. Thus:

f(x)=5x+4\\-(f(x))=-(5x+4)

Simplify:

-f(x)=-5x-4

B) To flip a function over the y-axis, change the variable x to -x. Thus:

f(x)=5x+4\\f(-x)=5(-x)+4

Simplify:

f(-x)=-5x+4

C) A reflection over the line y=x is synonymous with finding the inverse of the function.

To find the inverse, switch x and f(x) and solve for f(x):

f(x)=5x+4

Switch:

x=5f^{-1}(x)+4

Subtract 4 from both sides:

x-4=5f^{-1}(x)

Divide both sides by 5:

f^{-1}(x)=\frac{x-4}{5}

And we're done :)

7 0
3 years ago
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