Mathematics
Which of the following equations has two real and distinct roots ?
x2 - 5x + 6 = 0
x2 - 3x + 6 = 0
x2 - 2x + 5 = 0
x2 - 4x + 6 = 0
Quadratic Equations
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Answer
Comparing equation x2 - 5x + 6 = 0, with ax2 + bx + c = 0, we get :
a = 1, b = -5 and c = 6.
By formula,
D = b2 - 4ac
= (-5)2 - 4 × 1 × 6
= 25 - 24
= 1; which is positive.
Since, a, b and c are real numbers; a ≠ 0 and b2 - 4ac > 0
∴ Roots are real and distinct.
Hence, Option 1 is the correct option.
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