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lbvjy [14]
2 years ago
14

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

Mathematics
1 answer:
Anna35 [415]2 years ago
7 0

Step-by-step explanation:

they're is a neat little trick.

but first of all, "roots" means the 0 solutions of the equation. like

ax² + bx + c = 0

there are 2 solutions for x to make the whole expression equal 0.

these are the "roots".

now to the little trick :

when is a multiplication resulting in 0 ?

when at least one of the factors is 0.

and any quadratic expression can be written as multiplication of 2 factors. like

c(x - a)(x - b) = cx² - cax - cbx + cab

what are the "roots" or 0 points ?

either

c = 0

x - a = 0 | x = a

x - b = 0 | x = b

the leading coefficient = 3.

that means nothing else than c = 3.

root = 1 means (x - 1) is one factor.

root = -5 means (x + 5) is the other factor.

so, we have

3(x - 1)(x + 5) = 3x² + 12x - 15

and the equation is

3x² + 12x - 15 = 0

or

3x² + 12x = 15

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Answer:

x=4 orx=- 8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

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Step 2: Subtract -x^2+32 from both sides.

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5 0
3 years ago
Read 2 more answers
At an auditorium, 3 1/2 sections are filled with people watching a play. Exactly 3/5 of the people watching the play are parents
worty [1.4K]

Answer:

Fraction[Total number of sections filled filled with parents] = 2¹/₁₀ section

Step-by-step explanation:

Given:

Total number of sections filled = 3¹/₂ = 7 / 2 sections

Number of fraction parents watching play = 3/5

Find:

Fraction[Total number of sections filled filled with parents]

Computation:

Fraction[Total number of sections filled filled with parents] = Total number of sections filled x Number of fraction parents watching play

Fraction[Total number of sections filled filled with parents] = [7/2] x [3/5]

Fraction[Total number of sections filled filled with parents] = 21 / 10 sections

Fraction[Total number of sections filled filled with parents] = 2¹/₁₀ section

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IgorLugansk [536]

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Area = length × breadths

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If x = 5 cm, y = 12 cm, and z = 13 cm, what is the surface area of the geometric shape formed by this net?
Lera25 [3.4K]

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the answer is C.  210 sq. cm

Step-by-step explanation:

Find the area of the triangle

The area of one of the triangular faces can be found by using the formula below.  

a = 1/2 bh

a = 1/2 (5 cm) (12 cm)

a = 30 sq. cm

Since there are two triangular faces, multiply the area of one triangular face by 2. The area of two triangular faces is 60 cm2.

Next, find the area of each of the three rectangular faces using the formula, area = lw.

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2nd rectangle

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3rd rectangle

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a = (5 cm) (13 cm)

a - 65 sq. cm

Add the three rectangle areas to find a total of 150 sq. cm.

To find the surface area of the triangular prism, add the area of the two triangular faces to the area of the three rectangular faces.

60 sq. cm + 150 sq. cm = 210 sq. cm

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Describe the relationship between x and why in a line with negative slope
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In a line with negative slope, as x increase, y decreases.

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3 years ago
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