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Maths-

General

Easy

Question

If the roots of the equation $blank x to the power of 2 end exponent minus 2 a x plus a to the power of 2 end exponent plus a minus 3 equals 0$ are less than 3, then

$a < 2$
$2 \leq a \leq 3$
$3 < a \leq 4$
$a > 4$

The correct answer is: $a less than 2$

Since roots are less than a real number, roots must be real
$table row cell 4 a to the power of 2 end exponent minus 4 open parentheses a to the power of 2 end exponent plus a minus 3 close parentheses greater or equal than 0 end cell row cell rightwards double arrow a less or equal than 3 end cell end table$
$text Let end text f left parenthesis x right parenthesis equals x to the power of 2 end exponent minus 2 a x plus a to the power of 2 end exponent plus a minus 3 text . Since end text 3 text lies outside the roots end text$
Sum of the roots must be less than 6
2a < 6 ⇒ a < 3
From Eqs. (1)−(3), we have
a < 2

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