melanieambrosy
Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Find k so that 9x^2-48x+k is the square of a binomial.

Sagot :

DWRead

Answer:

Step-by-step explanation:

The discriminant must be zero.

Discriminant = (-48)^2 - 4*9k = 2304 - 36K

36k = 2304

k = 64

Using the square of a subtraction, it is found that k = 64.

What is a square of a subtraction?

It is a notable product, given by:

[tex](ax - b)^2 = a^2x^2 - 2abx + b^2[/tex]

In this problem, the expression is:

[tex]9x^2 - 48x + k[/tex]

We want it to be the square of a binomial, hence:

[tex]a^2x^2 - 2abx + b^2 = 9x^2 - 48x + k[/tex]

Then, comparing both sides, first the value of a is found:

[tex]a^2 = 9[/tex]

[tex]a = \sqrt{9}[/tex]

[tex]a = 3[/tex]

Then, with the second term, the value of b is found.

[tex]2ab = 48[/tex]

[tex]6b = 48[/tex]

[tex]b = \frac{48}{6}[/tex]

[tex]b = 8[/tex]

Finally, the value of k is found.

[tex]k = b^2 = 8^2 = 64[/tex]

You can learn more about the square of a subtraction at https://brainly.com/question/9239489

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.