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MArishka [77]
3 years ago
5

Write a standard form of a quadratic equation that has roots - 5/2 and 3.

Mathematics
1 answer:
lora16 [44]3 years ago
6 0

Answer:

2x^2 - x - 15 = 0.

Step-by-step explanation:

In factor form this is

(x + 5/2)(x - 3) = 0

x^2 + 5/2x - 3x  - 15/2 = 0

x^2 - 1/2x - 15/2 = 0

Multiply through by 2:

2x^2 - x - 15 = 0.

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Let <img src="https://tex.z-dn.net/?f=%5Csf%20a%2Bb%2Ca-b%2Cab%2C%5Cdfrac%7Ba%7D%7Bb%7D" id="TexFormula1" title="\sf a+b,a-b,ab,
Black_prince [1.1K]

Answer:

  • 171/40 or 4 11/40

Step-by-step explanation:

<h3>AP given</h3>
  • a + b, a - b,  ab, a/b
<h3>To find</h3>
  • 6th term
<h3>Solution</h3>

Common difference

<u>Difference of first two</u>

  • d = (a -b) - (a + b) = -2b

<u>Difference of second two</u>

  • d= ab - (a - b)

<u>Difference of last two</u>

  • d = a/b - ab

<u>Now comparing d:</u>

  • -2b = ab - (a - b)
  • ab - a = - 3b
  • a(1 - b) = 3b
  • a = 3b/(1 - b)

and

  • a/b - ab = -2b
  • a(1/b - b) = -2b
  • a = 2b²/(b² - 1)

<u>Eliminating a:</u>

  • 2b²/(b² - 1) = 3b/(1 - b)
  • 2b/(b+1) = -3
  • 2b = -3b - 3
  • 5b = - 3
  • b = -3/5

<u>Finding a:</u>

  • a = 3b/(1 - b) =
  • 3*(-3/5) *1/(1 - (-3/5)) =
  • -9/5*5/8 =
  • -9/8

<u>So the first term is:</u>

  • a + b = -3/5 - 9/8 = -24/40 - 45/40 = - 69/40

<u>Common difference:</u>

  • d = -2b = -2(-3/5) = 6/5

<u>The 6th term:</u>

  • a₆ = a₁ + 5d =
  • -69/40 + 5*6/5 =
  • -69/40 + 240/40 =
  • 171/40 = 4 11/40
8 0
3 years ago
Please help me answer this ​
jonny [76]
The answer is 112 im pretty sure!
4 0
3 years ago
Find the amount in the account.
Irina-Kira [14]

Answer:

I think it's D

Step-by-step explanation:

3 0
3 years ago
During a sale, for each shirt that Mark purchased at the regular price, he also purchased a shirt at half the regular price. How
Arisa [49]
I think the answer is b hope i helped
4 0
3 years ago
What is the factored form of x^2 - 4x - 5?
ser-zykov [4K]

we are given

x^2-4x-5

we can use formula

x^2-(a+b)x+ab=(x-a)(x-b)

so, we have

a+b=4

ab=-5

now, we can solve for a and b

and we get

a=5, b=-1

now, we can plug it in formula

x^2-4x-5=(x-5)(x+1) ............Answer

4 0
3 years ago
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