Which of the following are quadratics? For those that are,

Kathy Williams

Kathy Williams

Answered question

2021-12-14

Which of the following are quadratics? For those that are, identify the values of a, b, and c
1) 2x2+7x=15
2) x(x2+3x10)=0
3) (x+1)2=2(x3)
4) (x1)2+3=2x+1

Answer & Explanation

Hector Roberts

Hector Roberts

Beginner2021-12-15Added 31 answers

Step 1
The quadratic equations are of the form ax2+bx+c=0
To find a, b, c for the given equation if they are quadratic
Step 2
2) 2x2+7x=15
2x2+7x15=0 is qudratic
comparing it with ax2+bx+c=0
So, a=2, b=7, c=15
Step 3
2) The given equation is
x(x2+3x10)=0
x3+3x210x=0
Which is not a quadratic because the degrec of polynomial is 3
Step 4
3) The given equation is:
(x+1)2=2(x3)
x2+2x+1=2x6
x2+1+6=0
x2+7=0
Which is of degree 2
So, it is a quadratic equation
Comparing it with ax2+bx+c=0
a=1, b=0, c=7
Step 5
The given equation is:
(x1)2+3=2x+1
x22x+1=2x+1
x2+0
Which is of degree 2
So, it is quadratic equation
Comparing it with ax2+bx+c=0
a=1, b=0, c=0

usaho4w

usaho4w

Beginner2021-12-16Added 39 answers

Step 1
1) 2x2+7x=15
Subtract 15 from both sides of the equation
2x2+7x15=1515
Subtracting 15 from itself leaves 0.
2x2+7x15=0
This equation is in standard form: ax2+bx+c=0
Substitute 2 for a, 7 for b, and -15 for c.
3) x+1)2=2(x3)
Use binomial theorem (a+b)2=a2+2ab+b2 to expand (x+1)2
x2+2x+1=2(x3)
Use the distributive property to multiply 2 by x3
x2+2x+1=2x6
Subtract 2x from both sides
x2+2x+12x=6
Combine 2x and -2x to get 0
x2+1=6
Add 6 to both sides
x2+1+6=0
Add 1 and 6 to get 7
x2+7=0
This equation is in standard form: ax2+bx+c=0 Substitute 1 for a, 0 for b, and 7 for c.
4) (x1)2+3=2x+1
To expand (x1)2
x22x+1+3=2x+1
Add 1 and 3 to get 4.
x22x+4=2x+1
Subtract 2x from both sides.
x22x+42x=1
Combine -2x adn -2x to get -4x
x24x+4=1
Subtract 1 from both sides.
x24x+41=0
Subtract 1 from 4 to get 3.
x24x+3=0
Substitute 1 for a, -4 for b, and 3 for c.
Equation (2) is not a quadratic equation

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