Answer to Question #163833 in Algebra for Hadden

Question

. If 2x² + px + 1 ≥ -17/18 then p = ?

                A. ± 5               B. -5                       C. 5               D.√42

Answer 1

To prove: The equation x2+px−1=0 has real and distinct roots for all real values of p.
Consider x2+px−1=0
Discriminant D=p2−4(1)(−1)=p2+4
We know p2≥0 for all values of p
⇒p2+4≥0 (since 4>0)
Therefore D≥0
Hence the equation x2+px−1=0 has real and distinct roots for all real values of p.

P= 1_ 35/18

= ans is (c) 5