State whether the following quadratic equations have two distinct… - Vidyadip

Question

State whether the following quadratic equations have two distinct real roots. Justify your answer.
$2x^2 + x - 1 = 0.$

✓

Answer

Main concept used:
Quadratic equation $ax^2 + bx + c = 0$ will have two distinct real roots if $D > 0 or b^2 - 4ac > 0.$
$2x^2 + x - 1 = 0$
Now, $D = b^2 - 4ac$
$= (1)^2 - 4(2)(-1) (a = 2, b = 1, c = -1)$
$= 1 + 8$
$\Rightarrow D = 9 > 0$
$\therefore\ \text{D}> 0$
So, the given equation has two distinct real roots.

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