Question
State whether the following quadratic equations have two distinct real roots. Justify your answer.
$x2 - 3x + 4 = 0$
$x2 - 3x + 4 = 0$
✓
Answer
Main concept used:
Quadratic equation $ax^2 + bx + c = 0$ will have two distinct real roots if $D > 0 or b^2 - 4ac > 0.$
Given quadratic equation is $x^2 - 3x + 4 = 0$
Now, $D = b^2 - 4ac$
$= (-3)^2 - 4(1)(4) (a = 1, b = -3, c = 4)$
$\Rightarrow D = 9 - 16$
$\Rightarrow D = -7 < 0$
$\therefore$ D < 0
So, the given equation has no real roots.
Quadratic equation $ax^2 + bx + c = 0$ will have two distinct real roots if $D > 0 or b^2 - 4ac > 0.$
Given quadratic equation is $x^2 - 3x + 4 = 0$
Now, $D = b^2 - 4ac$
$= (-3)^2 - 4(1)(4) (a = 1, b = -3, c = 4)$
$\Rightarrow D = 9 - 16$
$\Rightarrow D = -7 < 0$
$\therefore$ D < 0
So, the given equation has no real roots.
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