Find p and q such that \(\displaystyle{x}^{{2}}+{p}{x}+{q}{

Darian Silva

Darian Silva

Answered question

2022-04-14

Find p and q such that x2+px+q<xx(1,5)

Answer & Explanation

glajusv8iv

glajusv8iv

Beginner2022-04-15Added 10 answers

First rearrange as follows:
x2+px+q<xx2+(p1)x+q<0
Recall from the properties of parabolas that
ax2+bx+c<0
between the (real) roots of the equation if a>0. So since in our case a=1>0, the parabola
x2+(p1)x+q<0
between its zeros. So since we are given that x(1,5) is the solution set, we surmise from above that
x2+(p1)x+q=(x1)(x5)=x26x+5p=5 and q=5

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