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1 year ago

What is the polynomial function of lowest degree with rational real coefficients and roots 2 and squared root 5?

Mathematics

1 answer:

Natalija [7]1 year ago

8 0

The polynomial having the above quantities is expressed as x³ - 2x² - 5x + 10 = 0

The above situations will form a Cubic polynomial. A Cubic polynomial function may be defined as an expression which can be written in the form of ax³ + bx² + cx + d = 0 where a, b, c and d are coefficients and x is the independent variable. Since, the polynomial should have real coefficients so its multiplicity will be equal to 1. Now, the roots of the polynomial are given as 2 and √5. Since, square roots always occur in pair so the polynomial will have -√5 as its root. Now, the polynomial formed will be

(x - 2) (x - √5) (x + √5) = 0

(x - 2) (x² - 5) = 0

x³ - 5x - 2x² + 10 = 0

=> x³ - 2x² - 5x + 10 = 0 which is the required polynomial.

Learn more about Polynomial at:

brainly.com/question/11911893

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Remember that:

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8 0

3 years ago

Read 2 more answers

A total of $76,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds

Anestetic [448]

Answer:

The amount invested as certificates of deposit is $ 35,000 and The amount invested as bonds is $ 41,000

Step-by-step explanation:

Given as :

The total amount to be invested as bonds and certificates of deposit (CD) = $76,000

Let the amount invested as bonds = $ x + $6000

And The amount invested as CD = $ x

Now, According to question

The amount invested as CD + The amount invested as bonds = $ x + $ x + $6000

Or, $ x + $ x + $6000 = $76,000

Or, $ 2x = $76,000 - $6000

So, $ 2x = $70,000

∴ x = $\frac{70000}{2}$ = $ 35,000

And $ x + $6000 = $ 35,000 + $6000 = $ 41,000

Hence The amount invested as certificates of deposit is $ 35,000 and The amount invested as bonds is $ 41,000 Answer

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3 years ago

A triangle has sides of length 5, 8, and 10. What is the measure of its largest angle?

masha68 [24]

We'll use the Law of Cosines
We'll call
side a = length 5
side b = length 8
side c = length 10
and their corresponding angles as A, B and C
"C" would be the largest angle
cos (C) = (a^2 + b^2 - c^2) / 2 * a * b
cos (C) = (5^2 + 8^2 - 10^2) / 2 * 5 * 8
cos (C) = 25 + 64 -100 / 80
cos (C) = -11 / 80
cos (C) = -0.1375 
arc cosine ( -0.1375 ) = 97.903 Degrees
The largest angle is 97.903 Degrees

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3 years ago

Viete's Formulas - what are they used for?

kozerog [31]

For quadratics, these formulas are used mainly for factoring.

Your equation can be written as ...

... 2(x² +2x -3) = 0

You factor this by looking for factors of -3 (c=x1·x2) that add to give +2 (b=-(x1+x2)). These are {-1, +3}, so the factorization is ...

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The roots are then 1 and -3, which sum to -b = -2.

(You will note that the numbers used in the binomial factors are the opposites of the roots x1 and x2 in the Viete's Formulas. That is how we can look for them to sum to "b", rather than "-b".)

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3 years ago