Question

Determine interval of 'a' for which the graph of the quadratic expression $x^2+\left(a-1\right)x+16$ always lie above x-axis for all real $x$.

• A. $\Rightarrow a\in (-7,9)$
• B. $\Rightarrow a\in (-9,9)$
• C. $\Rightarrow a\in (0,9)$
• D. $\Rightarrow a\in (-7,0)$

Answer 1

The correct option is A $\Rightarrow a\in (-7,9)$

It always lies above x-axis, if its descriminant is less than zero

$\Rightarrow (a-1{)}^2<4.16$

$\Rightarrow (a-1{)}^2-64<0$

$\Rightarrow a-1\in (-8,8)$

$\Rightarrow a\in (-7,9)$