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
kotykmax [81]
2 years ago
9

. If α and β are the roots of

Mathematics
2 answers:
Lostsunrise [7]2 years ago
5 0

Answer:

18x^2+85x+18 = 0

Step-by-step explanation:

<u><em>Given Equation is </em></u>

=> 2x^2+7x-9=0

Comparing it with ax^2+bx+c = 0, we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β = -\frac{b}{a}

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

<em>Now, Finding the equation whose roots are:</em>

α/β ,β/α

Sum of Roots = \frac{\alpha }{\beta } + \frac{\beta }{\alpha }

Sum of Roots = \frac{\alpha^2+\beta^2  }{\alpha \beta }

Sum of Roots = \frac{(\alpha+\beta )^2-2\alpha\beta   }{\alpha\beta  }

Sum of roots = (\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}

Sum of roots = \frac{49}{4} + 9 /\frac{-9}{2}

Sum of Roots = \frac{49+36}{4} / \frac{-9}{2}

Sum of roots = \frac{85}{4} * \frac{2}{-9}

Sum of roots = S = -\frac{85}{18}

Product of Roots = \frac{\alpha }{\beta } \frac{\beta }{\alpha }

Product of Roots = P = 1

<u><em>The Quadratic Equation is:</em></u>

=> x^2-Sx+P = 0

=> x^2 - (-\frac{85}{18} )x+1 = 0

=> x^2 + \frac{85}{18}x + 1 = 0

=> 18x^2+85x+18 = 0

This is the required quadratic equation.

dem82 [27]2 years ago
5 0

Answer:

α/β= -2/9      β/α=-4.5

Step-by-step explanation:

So we have quadratic equation  2x^2+7x-9=0

Lets fin the roots  using the equation's  discriminant:

D=b^2-4*a*c

a=2 (coef at x^2)   b=7(coef at x)  c=-9

D= 49+4*2*9=121

sqrt(D)=11

So x1= (-b+sqrt(D))/(2*a)

x1=(-7+11)/4=1   so   α=1

x2=(-7-11)/4=-4.5    so  β=-4.5

=>α/β= -2/9       => β/α=-4.5

You might be interested in
Which function is increasing at the highest rate?
patriot [66]

Answer:

D

-6y= -12x-24

/6          /6

change to slope intercept form: y=2x+4

slope is 2

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Can someone help me on this too!
Ann [662]

Answer:

72 signs

Step-by-step explanation:

90 min = 1.5 hour

6 hours hangs 6/1.5 * 18 signs = 72

3 0
3 years ago
Read 2 more answers
(m+3n) ^2 please help me solve this question, I really need it
Charra [1.4K]

Answer:

=m2+6mn+9n2

Step-by-step explanation:

=(m+3n)(m+3n)

=(m)(m)+(m)(3n)+(3n)(m)+(3n)(3n)

=m2+3mn+3mn+9n2

7 0
3 years ago
Is 1.32 a rational number or integer
Ivahew [28]

Answer:

A rational number.

Step-by-step explanation

A rational number is a ratio of whole numbers.

1/3 is the ratio of 1:3

3:1 becomes 3/1 = 3

32:10 can be written 32/10 or 16/5 or 3.2

16/5 is a rational number 16 and 5 are integers, 5 is not equal to 0.

Therefore, 3.2 which can be expressed as 16/5 is a rational number.

6 0
3 years ago
I desperately need this question answered. See attached image thanks so much
Dahasolnce [82]

For this case we must follow the steps below:

step 1:

We place each of the given points on a coordinate axis

Step 2:

We join the AC points (represented by the orange line)

We join the BD points (represented by the blue line)

It is observed that the resulting figure after placing the 4 points on a coordinate axis, turns out to be a rhombus.

In addition, the blue and orange lines turn out to be perpendicular, that is, they have an angle of 90 degrees between them. This can be verified by finding the slopes of each of the two straight lines (blue and orange), which must be opposite reciprocal, that is, they comply: m1 * m2 = -1

In this case, the slope of the orange line is m1 = 1 and that of the blue line is m2 = -1

Then m1 * m2 = 1 * -1 = -1, it is verified that they are perpendicular.

Thus, the conclusion is that ABCD is a rhombus and AC is perpendicular to BD.

Answer:

See attached image

Option D

6 0
3 years ago
Other questions:
  • A man can walk from A to B and back in a certain time at 7 km/hr.If he walks from A to B at 8 km/hr and returns from B to A at 6
    14·1 answer
  • Find 631.44 * 6.314 and round your answer to the nearest thousandth.
    10·1 answer
  • What is the point-slope form and standard form of (3,1) and (4, 2)?
    8·1 answer
  • Four less than five times a number is equal to 11
    12·2 answers
  • Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain. Mean for
    7·1 answer
  • A line segment has an end point of ( -4,-6) which reflection will produce an image with endpoints (-4, 6) and (-6,-4)
    6·1 answer
  • Giving brainliest !!!
    14·1 answer
  • Which equation represents a line that passes through (2,-1) and has a slope of 3?
    11·1 answer
  • Kevin is making hamburger patties for a family reunion. If he has 12_1/2 pounds of hamburger meat, how many 1/4 pound hamburger
    14·2 answers
  • Solve the equation 4(p+5) = 21.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!