All categories

3 years ago

If a quadratic equation with real coefficients has a discriminant of 3 then the two roots must be

Mathematics

1 answer:

lukranit [14]3 years ago

6 0

In a quadratic equation

q(x) = ax^2 + bx + c

The discriminant is = b^2 - 4ac

We have that discriminant = 3

If b^2 - 4ac > 0, then the roots are real.

If b^2 - 4ac < 0 then the roots are imaginary

In this problem b^2 - 4ac > 0 3 > 0

then the two roots must be real

You might be interested in

Write a recursive formula and an explicit formula for the following arithmetic sequence.

xenn [34]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

11, 13, 15, 17, 19, ...

Determining the Recursive formula:

We know that a recursive formula is termed as a formula that specifies each term of the given sequence using the preceding terms.

From the given sequence it is clear that every term can be obtained by adding two to the previous term.

i.e. 13 = 11+2, 15 = 13+2, 17 = 15+2, 19 = 17+2

aₙ₊₁ = aₙ+2, for n ≥1

Therefore, a recursive formula is:

aₙ₊₁ = aₙ+2, for n ≥1

Determining the Explicit formula:

Given the sequence

11, 13, 15, 17, 19, ...

An arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$

computing the differences of all the adjacent terms

$3-11=2,\:\quad \:15-13=2,\:\quad \:17-15=2,\:\quad \:19-17=2$

The difference between all the adjacent terms is the same and equal to

$d=2$

also

$a_1=11$

so substituting $d=2$ , $a_1=11$ in the nth terms

$a_n=a_1+\left(n-1\right)d$

$a_n=2\left(n-1\right)+11$

$a_n=2n+9$

Therefore, the Explicit formula is:

$a_n=2n+9$

4 0

2 years ago

What is the answers

LenKa [72]

If x=5 the answer is 0

3 0

3 years ago

Z1 and Z2 are vertical angles. Z2 has a measure of 31º. What is the measure of Z1

kogti [31]

Answer:

whatever 31-18 is i think

Step-by-step explanation:

5 0

3 years ago

teacher gives 5 students a multiple choice test, in which each problem is worth 1 point and there is no penalty with negative po

mamaluj [8]

The mean is the average value of a given set of numbers, and the median is the number in the middle of a set of numbers arranged in increasing order

The correct values as response to the questions are;

The minimum possible top score is 21

The maximum possible top score is 32

The minimum of the possible standard deviation is approximately 1.26

The maximum of the possible standard deviation is approximately 11.7

The reason the above values are correct are as follows:

The given parameters are;

The number of students that take the test, n = 5

The amount of points for each problem = 1 point

The median score = 9

The mean Score = 10

Required:

The minimum possible score;

The maximum possible top score

The minimum of the possible standard deviations

The maximum of the possible standard deviations

Solution:

Given that there is a score (the median) which is 9, we have;

The scores obtainable in the test is Scores ≥ 9

Therefore, for a score of 10, we have;

The minimum total points obtainable = Mean × Number of students

Therefore;

Total minimum total points obtainable by the 5 students = 5 × 10 = 50

The minimum possible top score

By arrangement, with the median at the middle, the minimum possible top score is given as follows;

0, 0, 9, 20, 21

Therefore, the minimum possible top score is 21

The maximum possible top score

The maximum possible top score is similarly given by arrangement of the numbers as follows'

0, 0, 9, 9, 32

The maximum possible top score is 32

The minimum standard deviation

By arrangement and selection, the minimum standard deviation is given as follows;

The minimum of the possible standard deviations of (9, 9, 9, 11, 12) ≈ 1.26

The maximum of the possible standard deviation

The maximum of the possible standard deviation is given as follows;

The maximum of the possible standard deviation of (0, 0, 9, 9, 32) ≈ 11.7

Learn more about mean and median here:

brainly.com/question/17012793

8 0

2 years ago

Which is the upper left quadrant on the coordinate plane?

Lisa [10]

Answer:

the upper left Quadrant is Quadrant II

4 0

3 years ago

Read 2 more answers