Quadratic Equation - gkquestionsguru.com

In the following questions, two equations numbered I and II are given. You have to solve both the equations and Give Answer If

x² + 25x + 156 =0
y²+27y+182 =0

If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or no relation can be established between ‘x’ and ‘y’.

Ans:2
I. x² + 25x + 156 =0X² + 12x + 13x +156 =0

(x+12) (x+13) =0

x = -12, -13

II. y²+27y+182 =0

Y² + 14y + 13y + 182 =0

(y+13) (y+14) =0

y =-13, -14

x ≥ y

4x+2y =14
3x+6y =24

If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or no relation can be established between ‘x’ and ‘y’.

Ans:3
4x+2y =14 —– (1)
3x+6y =24 —– (2)
Solve the equation, we get x = 2 and y =3

x = ∛1728
y = √(√20736)

If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or no relation can be established between ‘x’ and ‘y’.

Ans:5
I. x = ∛1728
x=12
II. y = √(√20736)
y= √144
y = 12
x=y

(x² – 12²) =0
y = ∛2197

If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or no relation can be established between ‘x’ and ‘y’.

Ans:3
I. (x² – 12²) =0(x+12) (x-12) =0

x=12, -12

II. y = ∛2197

y =13

x < y

4x+6y = 6
2x-3y =45

If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or no relation can be established between ‘x’ and ‘y’.

Ans:1
4x+6y = 6 —- (1)
2x-3y =45 —- (2)
Solve the equations, we get x = 12 and y = -7
x> y

Directions:6-10) In the following questions, two equations numbered I and II are given. You have to solve both questions and give answer among the following options.

4x²-4x-48=0
6y²-6y-12=0

if x>y
if x≥y
if x<y
if x≤y
if x=y or the relationship cannot be established)

Ans:5
I.4x²-4x-48=0
4x²-16x+12x-48=0
X=4,-3
II.6y²-6y-12=0
6y²+6y-12y-12=0
Y=2,-1
Thus relationship can’t be established

3x²+53x+204=0
5y²+31y+48=0

if x>y
if x≥y
if x<y
if x≤y
if x=y or the relationship cannot be established)

Ans:3
I.3x²+53x+204=0
3x²+36x+17x+204=0
X=-17/3 , -12
II.5y²+31y+48=0
5y²+15y+16y+48=0
Y=-16/5,-3
Thus y>x

2x²-39x+124=0
2y²-30y+108=0

if x>y
if x≥y
if x<y
if x≤y
if x=y or the relationship cannot be established)

Ans:5
I.2x²-39x+124=0
2x²-8x-31x+124=0
X=31/2, 4
II.2y²-30y+108=0
2y²-12y-18y+108=0
Y=9 ,6
Thus relationship can’t be established.

8x²-18x+9=0
y²+11y-432=0

if x>y
if x≥y
if x<y
if x≤y
if x=y or the relationship cannot be established)

Ans:5
I.8x²-18x+9=0
8x²-12x-6x+9=0
X=3/4, 3/2
II.y²+11y-432=0
y²+27y-16y-432=0
y=16,-27
Thus relationship can’t be established

10.

2x²+15x+28=0
4y²+32y+64=0

if x>y
if x≥y
if x<y
if x≤y
if x=y or the relationship cannot be established)

Ans:2
I.2x²+15x+28=0
2x²+8x+7x+28=0
X=-7/2 ,-4
II.4y²+32y+64=0
4y²+16y+16y+64=0
Y=-4 ,-4
Thus, X≥Y

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