Question

If $x^2+px+q=0$ is the quadratic equation whose roots are
$a–2$ and $b–2$ where $a$ and $b$ are the roots of $x^2-3x+1=0$, then

• A. None of these
• B. $p=-1,q=1$
• C. $p=1,q=-5$
• D. $p=1,q=5$

Answer 1

The correct option is A

None of these

$a+b=3,ab=1$ and $–p=a–2+b–2,q=(a–2)(b–2)$

$\Rightarrow –p=a+b–4,q=ab–2(a+b)+4$

$\Rightarrow$ $–p=3–4$ and $q=1–2\left(3\right)+4$
$\Rightarrow (p,q)=(1,–1)$