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3 years ago

I need help to solve this

Mathematics

1 answer:

sladkih [1.3K]3 years ago

5 0

Answer:

Step-by-step explanation:

The catch is to put this into the quadratic and solve for a b and c in three equations.

x = 1

a(1)^2 + b(1) + c= 0

a + b + c + 0 (1)

x = - 1

a(-1)^2 + b(-1) + c = 2

a - b + c = 2 (2)

x = 2

a(2)^2 + b(2) + c = 8

4a + 2b + c = 8 (3)

===================

Add 1 and 2 together

a + b + c = 0

a - b + c = 2

2a + 2c = 2 Divide by 2

a + c = 1 (4)

=====================

Multiply (2) by 2

2a - 2b + 2c = 4 (5)

======================

Add (5) + (3)

2a - 2b + 2c = 4

4a + 2b + c = 8

6a + 3c = 12 (6)

=====================

Multiply (4) by 3

3a + 3c = 3 (7)

===================

Subtract (7) from (6)

6a + 3c = 12

3a + 3c = 3

3a = 9 Divide by 3

3a/3 = 9/3

a = 3

=============

Use (4) to find c

a + c = 1

3 + c = 1 Subtract 3 from both sides

3-3 + c = 1-3

c = - 2

=================

Use 1 to find b

3 + b - 2 = 0 Combine 3 and -2

1 + b = 0 Subtract 1 from both sides

b = - 1

====================

Answers

a = 3

b = - 1

c = - 2

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