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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Sets and Relations

JEE Advanced · Mathematics · Sets and Relations

Let A=\ x x^3+x^2-p x+q=0, p, q, ∈ R\ and B=\ x x^2-q x+2=0, q ∈ R\...

Let A={x∣x3+x2−px+q=0,p,q,∈R}andA=\left\{x \mid x^3+x^2-p x+q=0, p, q, \in R\right\} andB=\left\{x \mid x^2-q x+2=0, q \in R\right\}bethesets.Ifbe the sets. Ifn(A \cap B)=2andandx_0 \in(A-B),thenfindthevalueof∣p−q+x0∣, then find the value of \left|p-q+x_0\right|. [Note: n(P∩Q)n(P \cap Q) denotes number of common elements in set PP and set QQ and a∈(P−Q)a \in(P-Q) denotes elements ' aa ' lies in set PP not in set QQ.]

Correct answer

3

Step-by-step solution

(x−x0)(x2−qx+2)=x3+x2−px+q⇒−x0−q=1,2+qx0=−p,−2x0=q⇒x0=1,q=−2,p=0∴∣p−q+x0∣=3\begin{aligned} & & \left(x-x_0\right)\left(x^2-q x+2\right) & =x^3+x^2-p x+q \\ \Rightarrow & & -x_0-q & =1,2+q x_0=-p,-2 x_0=q \\ \Rightarrow & & x_0 & =1, q=-2, p=0 \\ \therefore & & \left|p-q+x_0\right| & =3\end{aligned}
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