Keerthana
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I. 2x2+x28=02{x^2} + x - 28 = 0

II. 2y223y+56=02{y^2} - 23y + 56 = 0

a

If x > y

b

If x ≥ y

c

If y > x

d

If y ≥ x

e

If x = y or no relation can be established

Answer : Option D
Explanation :

I. 2x2+x28=02{{ m{x}}^2} + { m{x}} - 28 = 0

2x2+8x7x28=02{{ m{x}}^2} + 8{ m{x}} - 7{ m{x}} - 28 = 0

2x(x+4)7(x+4)=02{ m{x}}left( {{ m{x}} + 4} ight) - 7left( {{ m{x}} + 4} ight) = 0

(2x7)(x+4)=0left( {2{ m{x}} - 7} ight)left( {{ m{x}} + 4} ight) = 0

x=4,72x = - 4,frac{7}{2}II. 2y223y+56=02{{ m{y}}^2} - 23{ m{y}} + 56 = 0

2y216y7y+56=02{{ m{y}}^2} - 16{ m{y}} - 7{ m{y}} + 56 = 0

2y(y8)7(y8)=02{ m{y}}left( {{ m{y}} - 8} ight) - 7left( {{ m{y}} - 8} ight) = 0

(2y7)(y8)=0left( {2{ m{y}} - 7} ight)left( {{ m{y}} - 8} ight) = 0

y=72,8y = frac{7}{2},8

yx{ m{y}} ge { m{x}}

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