Question

Find the value of P. If polynomial f(x) = px^2 + 4x + 3x – 4 and g(x) = x^2 + 4 + p are divided by (x – 3), then remainder in each case is same.​

Answer 1

Answer:

f(x) = px^3 + 4x^2 + 3x – 4

➝ x – 3 = 0

➝ x = 3

f(x) = p(3)^3 + 4(3)^2 + 3 × 3 – 4

${R_1}$ = 27p + 36 + 9 (–4)

${R_1}$ = 27p + 41

g(x) = x^3 – 4 + p

x = 3

g(3) = 3^3 – 4 + p

= 27 – 4 + p

${R_2}$ = 23 + p

${R_1}$ = ${R_2}$

➝ 27p + 41 = 23

➝ 26p = 23 – 41

➝ 26p = – 18

➝ p = –9/13

Hence, the value of p = –9/13.