Quadratic Equation Practice Problems

1) Question:

I) x²+5x-176=0

II) y²-9y-162=0

Options:

A) x=(-15,11), y= (18,-10)

B) x = y or the relationship can’t be determined

C) x=(-16,11), y= (18,-9)

D) x=(-15,13), y= (17,-10)

Answer: (B)

Solution:

x²+5x-176=0

x²+16x-11x-176=0

x(x+16)-11(x+16)=0

(x+16) (x-11)=0

x= -16,11

y²-9y-162=0

y²-18y+9y-162=0

y(y-18)+9(y-18)=0
(y-18) (y+9)=0

y= 18,-9

Therefore relationship can’t be established.

2) Question: 

I) x²+6x+9=0
II) 2y²+13y+21=0

Options:

A) x < y

B) x ≥ y

C) can’t be determined

D) x<=y

Answer: (B)

Solution:

x²+6x+9=0

x²+ 3x + 3x + 9 = 0

x(x + 3) + 3(x + 3) =0

(x + 3) (x + 3) = 0

x=-3, -3

2y²+13y+21=0

2y²+6y+7y+21=0

2y(y+3) +7(y+3) =0

(y+3) (2y+7) =0

y= -3, -3.5

Therefore x ≥ y

3) Question:

I) 3x²-13x+10=0
II) y²-22y+120=0

Solution:

3x²-13x+10=0

3x²-3x-10x+10 =0

3x(x-1) - 10(x-1)=0

(x-1) (3x-10)=0

x=1, 3.33

y²-22y+120=0

y²-10y-12y+120=0

y(y-10) -12(y-10)=0

(y-10) (y-12)=0

y=10,12

Therefore x < y

Answer: x < y

4) Question:

I) 3x²-7x+4=0
II) 2y²-9y+10=0

Solution: 

3x²-7x+4=0

3x²-3x-4x+4=03x(x-1) -4(x-1)=0

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

x= 1, 1.33

2y²-9y+10=0

2y²-4y-5y+10=0

2y(y-2) -5(y-2)=0

(y-2) (2y-5)=0

y= 2, 2.5

Therefore x < y

Answer: x < y

5) Question:

I) (x+8)²=36x-32
II) (y-12)²=6y-81

Solution: 

(x+8)²=36x-32

(x²+16x+64) =36x -32

x²-20x+96=0x²-12x-8x+96=0

x(x-12) -8(x-12)=0(x-12) (x-8) =0

x=12,8

(y-12)=6y-81

y²-24y+144-6y+81=0

y²-30y+225=0

y²– 15y – 15y + 225 = 0

y(y – 15) – 15(y – 15) = 0

(y-15)²=0

y=15, 15

Therefore x < y

Answer: x < y

6) Question:

I) x²- 4x – 21 = 0
II). y²- 8y +16 = 0

Solution:

x²- 4x – 21 = 0

(x – 7) (x + 3) = 0

X = 7, -3

y²-8y +16 = 0

(y - 4) (y – 4) = 0

Y = 4,  4

Answer: Can’t be determined

7) Question:

I) 2x²+ 13x + 21 = 0
II) 3y²+ 4y – 15 = 0 

Solution: 

2x²+ 13x + 21 = 0

2x²+ 6x + 7x + 21 = 0

2x (x + 3) + 7(x + 3) = 0

(2x + 7) (x + 3) = 0

x = -7/2, -3 =

x = -3.5, -3

3y²+ 4y – 15 = 0

3y²+ 9y - 5y – 15 = 0

3y (y + 3) -5(y + 3) = 0

(3y – 5) (y + 3) = 0

y = 5/3, -3 = 1.667, -3

x ≤ y

Answer: x ≤ y

8) Question:

I) 2x²- 19x + 35 =0
II) 2y²- 13y + 21 =0

Solution: 

2x² - 19x + 35 =0

2x² - 14x - 5x + 35 =0

2x(x - 7) - 5(x - 7) =0

(2x - 5)(x - 7) =0

x=7, 2.5

2y² - 13y + 21 =0

2y² - 6y - 7y + 21 =02y(y - 3) - 7(y - 3) =0

(2y - 7)(y - 3) =0

y=3, 3.5

Hence the relationship between x and y cannot be established.

Answer: the relationship between x and y cannot be established.

9) Question:

I) 4x²– 17x + 18 = 0
II) 3y²– 29y + 56 = 0

Solution: 

4x²– 17x + 18 = 0

=>4x² – 8x – 9x + 18 = 0

=>4x (x – 2) – 9 (x – 2) = 0

=>(4x – 9) (x – 2) = 0

=> x = 9/4, 2

3y² – 29y + 56 = 0

=>3y² –21y – 8y + 56 = 0

=> 3y (y – 7) – 8 (y – 7) = 0

=> (3y – 8) (y – 7) = 0

=> y = 8/3, 7

Hence, x < y

Answer: x < y

10) Question:

I).x²+18x=144
II).3y²+19y+26=0

Solution:

x²+18x-144=0

x²+ 24x – 6x – 144 = 0

x(x + 24) – 6(x + 24) = 0

(x-6) (x+24)=0

x= 6, -24

3y²+19y+26=0

3y²+ 13y + 6y + 26 = 0

y(3y + 13) + 2(3y + 13) = 0

(y+2) (3y+13) =0

y= -2, -4.33

Relationship can’t be established

Answer: The relationship cannot be established.

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