Question

if the polynomial f(x) =px3+4x2+3x-4 and g(x) =x3-3+p are divided by ( x - 3) then the remainder in each case is same. find the value of p.​

Answer 1

Answer:

f(x) = px³ + 4x² +3x - 4

g(x) = x³ - 3 +p

Now, (x-3) = 0;

∴ x = 3

let the remainder be "a";

∴ f(3) = p(3)³ + 4(3)² + 3(3) - 4 = a;

→ 27p + 36 + 9 - 4 = a

→ 27p + 41 = a ----- (i)

Now, g(3) = (3)³ - 3 + p = a;

→27 - 3 +p = a;

→24 + p = a; ----- (ii)

equate (i) & (ii)

27p + 41 = 24 + p;

27p - p = 24 - 41;

26p = -17;

p = -17/26;