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Question 10
Which of the following equations has no real roots?
(A)
x24x+32=0
(B) x2+4x32=0
(C) x24x32=0
(D) 3x2 43x+4=0

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Solution

a) The given equation is x24x+32=0
On comparing with ax2+bx+c=0, we get
A = 1, b = -4 and c = 32
The discriminant of x24x+32 = 0 is
D=b24ac
=(4)24(1)(32)=16122=1612×(1.41)
=1616.92=0.92
b24ac<0

b) The given equation is x2+4x32=0
On comparing with ax2+bx+c=0, we get
A = 1, b = 4 and c = 32
The discriminant of x2+4x32 = 0 is
D=b24ac
=(4)24(1)(32)=16+122=16+12×(1.41)
=16+16.92=32.92
b24ac>0

c) The given equation is x24x32=0
On comparing with ax2+bx+c=0, we get
A = 1, b = -4 and c = 32
The discriminant of x24x32 = 0 is
D=b24ac
=(4)24(1)(32)=16+122=16+12×(1.41)
=16+16.92=32.92
b24ac>0

d) The given equation is 3x243x+1=0
on comparing with ax2+bx+c=0, we get
A = 3, B = 43 and C = 4
The discriminant of 3x2 43x+4=0
D=b24ac
=(43)24(4)(3) = 4848 = 0

Therefore, only equation given in option (A) has no real roots.


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