RRB Assistant Loco Pilot and Technician Model Paper 6 with solutions

Since, HCF of the polynomials
${\mathit{x}}^3\mathit{–}3{\mathit{x}}^2$ + px + 24 and ${\mathit{x}}^2$ – 7x + q is x – 2 Here we put x = 2 in the given polynomials, we have
${\left(2\right)}^3$ – 3 × 22 + p × 2 + 24 = 0
⇒ 8 – 12 + 2p + 24 = 0
2p = – 20
∴ p = –10
Again, ${\left(2\right)}^2$ – 7 × 2 + q = 0
⇒ 4 – 14 + q = 0
⇒ –10 + q = 0
∴ q = 10
∴ p + q = –10 + 10 = 0