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Damm [24]
3 years ago
10

Write the quadratic equation whose roots are 3 and -1, and whose leading coefficient is 5.

Mathematics
1 answer:
Assoli18 [71]3 years ago
6 0

Answer:

5x² - 10x - 15 = 0

Step-by-step explanation:

Given that the roots are x = 3 and x = - 1, then the factors are

(x - 3) and (x + 1) and the quadratic is the product of the factors, that is

f(x) = a(x - 3)(x + 1) ← a is a multiplier

Here a = 5, thus

f(x) = 5(x - 3)(x + 1) ← expand factors using FOIL

     = 5(x² - 2x - 3) ← distribute parenthesis by 5

     = 5x² - 10x - 15

Thus equation is

5x² - 10x - 15 = 0

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Complete question :

designs a board game in which a card is drawn on each turn. • A blue card means move forward 4 squares. • A red card means move back 6 squares. Liam suggests adding some other cards to Sia's game Part A Liam explains that drawing a yellow card is equivalent to drawing a blue card followed by a red card. How many spaces forward or backward does a player move after drawing a yellow card? Justify your answer.

Answer:

2 squares backward

Step-by-step explanation:

Given the rule :

Blue card = 4 squares forward

Red card = 6 squares backward

Yellow card = drawing a blue followed by a red

Spaces moved after drawing a yellow card:

Yellow equals :

Blue = + 4 squares ; then

Red = - 6 squares

Net total movement :

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Step-by-step explanation:

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x + 4.3x \leq 125.75 is the inequality that describes this problem

<h3><u>Solution:</u></h3>

Given that Travis can spend no more  than $125.75 every month

To find: linear inequality that describes the problem

Let the amount spent on movies = x dollars

Given that Travis decided to spend 4.3 times as much  money on video games as he spends on movies

Amount spent on video games = 4.3 (amount spent on movies)

Amount spent on video games = 4.3x

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<em><u>Thus, the inequality representing the situation is:</u></em>

\text{ Amount spent on movies + Amount spent on video games } \leq 125.75

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Answer:

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