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.
$x(1 - x) - 2 = 0.$

✓

Answer

Main concept used:
Quadratic equation $ax^2 + bx + c = 0$ will have two distinct real roots if $D > 0 or b^2 - 4ac > 0.$
$x(1 - x) - 2 = 0$
$\Rightarrow x - x^2 - 2 = 0$
$\Rightarrow -x^2 + x - 2 = 0$
Now, $D = b^2 - 4ac$
$= (-12) - 4(-1) (-2)(a = -1, b = 1, c = -2)$
$= 1 - 8$
$\Rightarrow D = -7 < 0$
So, the given equation has no real roots.

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