Question

The entire graph of the equation $y=x^2+kx-x+9$ is strictly above the $x-$axis if and only if :

• A. $k<7$
• B. $-5<k<7$
• C. $k>-5$
• D. $noneofthese$

Answer 1

The correct option is B $-5<k<7$

$y=x^2+kx-x+9$

$a>0$

if $b^2-4ac<0$ & $a>0$

then the graph will always be above x-axis

$a=1\therefore a>0$.

$(K-1{)}^2-4\times 9<0$

$(K-1{)}^2-6^2<0$

$(K-1-6)(K-1+6)<0$

$(K-7)(K+5)<0$

$K>-5,K<7$

$-5<K<7$

Option B.