Mathematics
Which of the following equations has imaginary roots ?
x2 + 10x - 3 = 0
2x2 - 5x + 9 = 0
x2 + 5x + 4 = 0
5x2 - 8x - 1 = 0
Quadratic Equations
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Answer
Comparing equation x2 + 10x - 3 = 0, with ax2 + bx + c = 0, we get :
a = 1, b = 10 and c = -3.
By formula,
D = b2 - 4ac
= (10)2 - 4 × 1 × -3
= 100 + 12
= 112; which is positive.
Comparing equation 2x2 - 5x + 9 = 0, with ax2 + bx + c = 0, we get :
a = 2, b = -5 and c = 9.
By formula,
D = b2 - 4ac
= (-5)2 - 4 × 2 × 9
= 25 - 72
= -47; which is negative.
∴ Roots are imaginary.
Hence, Option 2 is the correct option.
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