Question

$I.p^2-8p+15=0II.q^2-5q=-6$

• A. p < q
• B. p > q
• C. p ≤ q
• D. p ≥ q
• E. p = q

Answer 1

The correct option is D p ≥ q

$\left(I\right)p^2-8p+15=0\Rightarrow p^2-3p-5p+15=0\Rightarrow p(p-3)-5(p-3)=0\Rightarrow (p-3)(p-5)=0\Rightarrow p=3or5\left(II\right)q^2-5q=-6\Rightarrow q^2-5q+6=0\Rightarrow q^2-3q-2q+6=0\Rightarrow q(q-3)-2(q-3)=0\Rightarrow q(q-3)(q-2)=0\Rightarrow q=3or2Obviously,p\ge q.$