Question

If 1/2 is a zero of the polynomial p(x) = 2x⁴ - mx³ + 4x² + 2x + 1, find the value of m.

Answer 1

Answer:

hey mate here is your answer,,......

Given ...

let p(x)= 2x4 - ax3 + 4x2 + 2x + 1 =0

1-2x=0 ==> -2x=-1 ==> x=1/2

p(1/2)= 2(1/2)4 - a(1/2)3 + 4(1/2)2 + 2.1/2 + 1 = 0

==>2.1/16 -a.1/8 +4.1/4 +2/2 +1 =0

hope it's helpful for you..,

thanks

Answer 2

Answer:

m = 25

Step-by-step explanation:

We have p(x) = 2x^4 - mx^3 + 4x^2 + 2x + 1.

One zero of the polynomial = (1/2).

Hence, p(1/2) = 0.

Place x = (1/2) in p(x).

p(1/2) = 2(1/2)⁴ - m(1/2)³ + 4(1/2)² + 2(1/2) + 1

=> 0 = 2(1/16) - m(1/8) + 4(1/4) + 1 + 1

=> 0 = 1/8 - m/8 + 1 + 1 + 1

=> m/8 = 1/8 + 1 + 1 + 1

=> m/8 = 25/8

=> m = 25

Thus the value of m is 25.

#Hope my answer help you.