Can someone show me steps to get the desired answer ?

Question

The desired answer is : $-1 < h < 7$

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Answer 1 · 2017-08-31T17:46:38

refer to explaination.

given:-
$x^2+(h-3)x+4$
here discriminant is less than 0.
since it's inequality.

so we know d= $b^2-4ac$
d= $h^2 +9 -6h -16$
d < 0; $h^2 -6h -7 <0$

use splitting the middle term.
h=-1,h=7

so ,h is a real no. varying from -1 to 7

$-1 <=h <=7$

hope it helps!!