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valina [46]
3 years ago
13

Please solve with full steps (only question 6)

Mathematics
1 answer:
Stels [109]3 years ago
8 0

Answer:

\large \boxed{\sf \ \ k=1 \ \ }

Step-by-step explanation:

Hello,

First of all, let's notice that even if we do not know the zeros of P(x) we can say that

       (1) \ \alpha + \beta =\dfrac{5}{6} \\ \\ (2) \ \alpha * \beta =\dfrac{k}{6}

<u>But, why !?</u>

As they are the zeros of P(x), we can write:

P(x)=6(x^2-\boxed{\dfrac{5}{6}}x+\boxed{\dfrac{k}{6}})=6(x-\alpha)(x-\beta)=6(x^2-\boxed{(\alpha +\beta)}x+ \boxed{\alpha *\beta} )

And then we can identify the coefficients of the like terms to find the equations (1) and (2).

Now, we have <u>one more equation</u> which is:

       (3) \ \alpha -\beta =\dfrac{1}{6}

(1)+(3) gives:

   \alpha + \beta +\alpha -\beta =\dfrac{5}{6}+\dfrac{1}{6}=\dfrac{6}{6}=1 \\ \\ 2\alpha =1 \ \text{ divide by 2 } \\ \\  \alpha =\dfrac{1}{2}

And we replace in (3) to get the value of the second zero.

   \beta = \dfrac{1}{2}-\dfrac{1}{6}=\dfrac{3-1}{6}=\dfrac{2}{6}=\dfrac{1}{3}

And, finally, from (2), it comes:

   k=6*\alpha *\beta =6*\dfrac{1}{2}*\dfrac{1}{3}=\dfrac{6}{6}=1

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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Solving 6x²+9x-1=0 by completing the square root method produces an equation in the form of (x+h)²=k find H and K
marishachu [46]

The value of h is 9/12 and the value of k is 35/48

<h3>How to solve the equation?</h3>

The equation is given as:

6x^2 +9x - 1 = 0

Add 1 to both sides of the equations

6x^2 +9x - 1 + 1= 0 + 1

Evaluate the sum

6x^2 +9x =  1

Divide through the equation by 6

x^2 +9/6x =  1/6

Take the coefficient of x

k = 9/6

Divide by 2

k/2 = 9/12

Square both sides

(k/2)^2 = (9/12)^2

So, we add (9/12)^2 to both sides of the equation x^2 +9/6x =  1/6

x^2 +9/6x + (9/12)^2 =  1/6 + (9/12)^2

Next, we express the left-hand side as a perfect square

(x^2 + 9/12)^2 = 1/6 + (9/12)^2

The form of the equation is given as:

(x + h)^2 = k

So, we have:

h = 9/12

k = 1/6 + (9/12)^2

Simplify

k = 1/6 + (3/4)^2

Evaluate the exponent

k = 1/6 + 9/16

This gives

k = (8 + 27)/48

Evaluate

k = 35/48

Hence, the value of h is 9/12 and the value of k is 35/48

Read more about completing the square at:

brainly.com/question/4331586

#SPJ1

5 0
1 year ago
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