Dear Student, We have,px=5x3+kx2+2x-14Now, p2 = 30 + p-1⇒523+k22+22-14 = 30+5-13+k-12+2-1-14⇒40+4k+4-14=30-5+k-2-14⇒4k-k=-21⇒3k=-21⇒k=-7 Regards!

Please solve it

Dear Student,

We have, p (x) = 5 x^{3} + {kx}^{2} + 2 x - 14 Now, p (2) = 30 + p (- 1) \Rightarrow 5 {(2)}^{3} + k {(2)}^{2} + 2 (2) - 14 = 30 + 5 {(- 1)}^{3} + k {(- 1)}^{2} + 2 (- 1) - 14 \Rightarrow 40 + 4 k + 4 - 14 = 30 - 5 + k - 2 - 14 \Rightarrow 4 k - k = - 21 \Rightarrow 3 k = - 21 \Rightarrow k = - 7

Regards!