MATHEMATICS: Solving Quadratics Functions(2)?

Question

Find:
a. roots of the function
b. zero of the function

1)x^2 - 5x + 6 = 0

2)x^2 - 10x = -21

3)x^2 - x -6 = 0

4)x^2 + 4x = 5

5)2x^2 + 2x = 4

6)-x^2 + 4x - 3=0

Show solutions / reasons. Thanks.

I'M SORRY! The question "find the zero of the function," kindly disregard that. Thanks again.

Answer 1

1)
x^2 - 5x + 6 = 0
(x-3)(x-2)= 0
x= 3, 2

2)
x^2 - 10x = -21
(x-7)(x-3)= 0
x= 7, 3

3)
x^2 - x -6 = 0
(x-3)(x+2)= 0
x= 3, -2

4)
x^2 + 4x = 5
(x+5)(x-1)= 0
x= -5, 1

5)
2x^2 + 2x = 4
x^2 + x - 2=0
(x+2)(x-1)= 0
x= -2, 1

6)
-x^2 + 4x - 3=0
x^2 -4x +3 =0
(x-1)(x-3)= 0
x= 1, 3

Answer 2

1)

x² - 5x + 6 = 0

x² - 2x - 3x + 6 = 0

x(x - 2) - 3(x - 2) = 0

(x - 3)(x - 2) = 0

Roots

x = 3 and x = 2

- - - - - - - -
2)

x² - 10x = - 21

x² - 10x + 21 = - 21 + 21

x² - 10x + 21 = 0

x² - 3x - 7x + 21 = 0

x(x = 3) - 7(x - 3) = 0

(X - 7)(X - 3) = 0

x = 7 and x = 3
- - - - - - - - - - - -
3)

x² - x - 6 = 0

x² + 2x - 3x - 6 = 0

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

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

Roots

x = 3 and x = - 2
- - - - - - - -
4)

x² + 4x = 5

x² + 4x - 5 = 5 - 5

x² + 4x - 5 = 0

x² - 1x + 5x - 5 = 0

x(x - 1) + 5(x - 1) = 0

(x + 5)(x - 1) = 0

Roots

x = - 5 and x = 1
- - - - - - - - -
5)

2x² + 2x = 4

Transpose 4

2x² + 2x - 4 = 4 - 4

2x² + 2x - 4 = 0

Common factor 2

2(x² + x - 2) = 0

2(x² - 1x + 2x - 2) = 0

2[x(x - 1) + 2(x - 1) = 0

2(x + 2)(x - 1) = 0

roots

2 = 0

x = - 2

x = 1
- - - - - - - - -
6)

- x² + 4x - 3 = 0

Multiply the equation by - 1

- (- 1)(x²) + (- 1)(4x) - (- 1)(3) = - 1(0)

- (- x²) + (- 4x) - (- 3) = 0

x² - 4x + 3 = 0

x² - 1x - 3x + 3 = 0

x(x - 1) - 3(x - 1) = 0

(x - 3)(x - 1) = 0

Roots

x = 3 and x = 1

- - - - - - - - -s-

Answer 3

x² - x - 1 = 0 x² - x + 1/4 = 1 + 1/4 (x - 1/2)² = 5/4 x - 1/2 = ±√5 / 2 x = 1/2 ± √5 / 2 (1/2 + √5 / 2)² - (1/2 + √5 / 2) - 1 = 0 1/4 + √5/2 + 5/4) - 1/2 - √5/2 - 1 = 0 6/4 - 6/4 + √5/2 - √5/2 = 0 0 = 0

Answer 4

1. =(x-2)(x-3)
x= 2 or 3

2. =(x-3)(x-7)
x = 3 or 7

3. =(x-3)(x+2)
x= 3 or -2

4. =(x+5)(x-1)
x = -5 or 1

5. =(x-2)(x+1)
x = 2 or -1

6. =(x-1)(x-3)
x = 1 or 3

all questions are the same just factorise using whatever method seems best to you. i use the "cross swords method" where u find the factors of the constant term and then work out what combination of adding or subtracting these will give u the coefficient of the "x" term. then for example if your factor is (x+3) you solve for x and get x= -3 and that is the root.

Answer 5

1) x^2 - 5x + 6 = 0
(x -2)(x-3)= 0
x = 2, 3
2) x^2 -10 x + 21 = 0
(x-7)(x-3)=0
x = 7, 3
3) x^2 -x -6 = 0
(x+2)(x-3)=0
x = -2, 3
4) x^2 + 4x - 5 = 0
(x+5)(x-1)=0
x= - 5 , 1
5) 2x^2 + 2x - 4 = 0
(2x - 2 )(x+2 )=0
x = 1, -2
6) -x^2 + 4x -3 = 0
x^2 - 4x + 3 = 0
(x -1)(x-3)=0
x=1, 3

Answer 6

(ax+b)(cx+d)=acx^2+(bc+ad)x+bd
Use this general factoring formula. If it doesn't work, use complete the square operation, or use quadratic equation to solve for x.
www.mymathforum.com is a good website for mathematics. You can post stuff in the forum, and people will reply back to you anytime. Please join it. Oh, and by the way... let me know by sending me a private message in the forum if you've joined the forum. My name in that forum is johnny.

Answer 7

roots as the same as zeros
1)(x-3)(x-2)=0
x=3 x=2
-------------------------------------
2)x^2-10x+21=0
(x-3)(x-7)=0
x=3 x=7
---------------------------------------
3)(x-3)(x+2)=0
x=3 x=-2
------------------------
4)x^2+4x-5=0
(x+5)(x-1)=0
x=-5 x=1
--------------------------
5)x^2+x-2=0
(x+2)(x-1)=0
x=-2 x=1
----------------------------------
6)x^2-4x+3=0
(x-3)(x-1)=0
x=3 x=1

Answer 8

I'm really rubbish at maths, it was my worst subject at school.. so I'm not even gonna attempt these!