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Question

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)

d) iv) Given equation is 3x2 – 4\sqrt{3}x + 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


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