Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Values of $'a'$ for which $x^{2}-ax+a\geqslant 0$ $\forall$ $x\; \epsilon \; R$ are

Option 1)
$a\: \epsilon R$

Option 2)
$a\: \epsilon \: \left ( 0,5 \right )$

Option 3)
$a\: \epsilon \: R^{+}$

Option 4)
$a\: \epsilon \: \left[0,4 \right ]$

Answers (1)

coeff of $x^{2}=1> 0$ , so only other required condition is $D\leqslant 0$

$\Rightarrow \: a^{2}-4a\leqslant 0$

$\Rightarrow \: a\, \epsilon \, \left [ 0,4 \right ]$

$\therefore$ Option (D)

Quadratic Expression ax^2 + bx + c is non negative -

$ax^{2}+bx+c\geqslant 0$ for all $x \epsilon R$ When $a> 0$ & $b^{2}-4ac\leq 0$ $\left ( \; a,b,c\; \epsilon\; R \right )$

-

Option 1)

$a\: \epsilon R$

This is incorrect

Option 2)

$a\: \epsilon \: \left ( 0,5 \right )$

This is incorrect

Option 3)

$a\: \epsilon \: R^{+}$

This is incorrect

Option 4)

$a\: \epsilon \: \left[0,4 \right ]$

This is correct

Posted by

Vakul

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question