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Quadratic Equations — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsQuadratic Equations2 Marks
Question
State whether the following quadratic equations have two distinct real roots. Justify your answer.
$3x^2 - 4x + 1 = 0.$
✓

Answer

Main concept used:
Quadratic equation $ax^2 + bx + c = 0$ will have two distinct real roots if $D > 0 or b^2 - 4ac > 0.$
$3x^2 - 4x + 1 = 0$
$Now, D = b^2 - 4ac (a = 3, b = -4, c = 1)$
$= (-4)^2 - 4(3)(1) = 16 - 12$
$\Rightarrow D = 4 > 0$
$\therefore\ \text{D}>0$
So, the given equation has two distinct real roots.

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