1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kipish [7]
3 years ago
8

Which two values of x are roots of the polynomial below x^2 - 11x + 13

Mathematics
2 answers:
matrenka [14]3 years ago
7 0

Because 13 is a prime number, we cannot use the AC method to simplify.

We can instead use the quadratic formula.

\frac{-b +/- \sqrt{b^2 - 4ac} }{2a}

11 +/- √121 - 52 / 2

11 +/- √69 / 2

11 +/- 8.3 / 2

(11 + 8.3)/2 = 9.65

(11 - 8.3)/2 = 1.35

<h3>The roots of the polynomial are 9.65 and 1.35.</h3>
Ad libitum [116K]3 years ago
3 0

Answer:

x=\frac{11+\sqrt{69}}{2} and x=\frac{11-\sqrt{69}}{2}

Step-by-step explanation:

x^2-11x+13

13 is a prime number . we cannot factor it because we cannot find two factors whose product is 13 and sum is -11. Apply quadatic formula to find the x values

Given polynomial is in the form of ax^2+bx+c

a= 1, b= -11 and c=13

x=\frac{-b+-\sqrt{b^2-4ac}}{2a}

Plug in the values in the formula

x=\frac{11+-\sqrt{(-11)^2-4(1)(13)}}{2(1)}

x=\frac{11+-\sqrt{69}}{2(1)}

x=\frac{11+\sqrt{69}}{2} and x=\frac{11-\sqrt{69}}{2}

You might be interested in
The last step in a proof contains the
Lemur [1.5K]

Answer:

Conclusion

Step-by-step explanation:

So you proved something Then you conclude something else)))

3 0
3 years ago
Read 2 more answers
1/4 times X -1+ 3X equals 2
iris [78.8K]

Answer:

41

Step-by-step explanation:

4 0
3 years ago
In how many ways can you park 4 different cars at a car park with 5 different parking spaces?
meriva
1. If you have 1 first then... 1,2,3,4 - 1,3,2,4 - 1,2,4,3 - 1,3,4,2 - 1,4,3,2 - 1,4,2,3
2. If you have 2 first the.... 2,1,3,4,- 2,1,4,3 - 2,3,1,4 - 2,3,4,1 - 2,4,3,1- 2,4,1,3
3. And so one with 3,4
Hope this helps:)
5 0
3 years ago
Describe how both the Rational Root Theorem and Descartes’ Rules of Signs help you to find the zeros of a polynomial? Give me an
MrRa [10]

Answer:

Step-by-step explanation:

Rational Root Theorem: If the polynomial

P(x) = a n x n + a n – 1 x n – 1 + ... + a 2 x 2 + a 1 x + a 0

has any rational roots, then they must be of the form of (factors of a0/factors of an).

Example: F(x) = 4x² + 5x +2

If this polynomial has any rational roots, then they must be (factors of 2)/(factors of 4), so (±1, ±2)/(±1, ±2, ±4). So if this polynomial has any rational roots, they must be either: ±1, ±1/2, ±1/4, or ±2. Notice that this polynomial doesn't have to have any rational roots, but if it does, then the roots must fit the Rational Root Theorem.

Descartes' Rules of Signs:

a). In a polynomial, how many time the sign changes is how many positive roots the polynomial will have.

Example: 5x³ + 6x² - 2x - 1

In this expression, the sign only changed once, between 6x² and 2x, so it will only have one positive root.

Example 2: 6x³ - 4x² + x - 6

In this expression, the sign changed 3 times (remember there is a invisible "+" sign before the 6x³), so it will have 3 positive roots.

b). In a polynomial, if you plug in "-x" for all "x", then how many times the new polynomial changes sign is how many negative roots the old polynomial have.

Example: 5x³ + 6x² - 2x - 1.

If we plug in "-x" for all "x", then we get 5(-x)³ + 6(-x)² - 2(-x) -1, which simplifies to -5x³ + 6x² + 2x -1. In this new expression, the sign changed twice, so we have two negative roots for the expression. Notice how we got one positive root the first time and two negative roots the second time, and 1 + 2 = 3. The Fundamental Theorem of Algebra states that for a nth degree polynomial, it will have n complex roots. The polynomial we worked with was a 3rd degree polynomial, and we got 1 + 2 = 3 roots in the end.

4 0
3 years ago
At a sale, coats were sold for 52% of their original price. If the coats originally cost $200 each, how much did a coat cost on
Talja [164]

Answer is 104

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • If lenny choose a time of day at random to turn on the radio to his favorite station ,l what is the probability that the news wi
    12·1 answer
  • Find the value of x. ladidada i need 20 characters
    6·1 answer
  • I’m begging for help!! ASAP
    10·1 answer
  • 91,007,500 in scientific notation
    9·2 answers
  • **********(*ˊᗜˋ*)ᵗᑋᵃᐢᵏ ᵞᵒᵘ********** This week Ivania ran a total of 20 km, which is 6.5 km farther than she ran last week. If w
    5·2 answers
  • What is the simplified expression for the expression below?<br>-3 (5x+20) - 1/4(4x-28)​
    8·1 answer
  • Simplify/solve the expression. 5+ (-5) +2 +10 +(-2)?
    6·2 answers
  • Um another Distributive Property question ahah,
    15·1 answer
  • A circular table has a radius of 5cm. Decorative trim is placed along the outside edge. How
    6·1 answer
  • Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the v
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!