Question

find the value of m if x=1/5 root 2 is zero of the polynomial p(x)=2x^2-7 mx+5

Answer 1

if 1/5√2 is a root of p(x),
then
p(1/5√2)=0,

2×(1/5√2)²-7×m×1/5√2 +5=0,

2×1/50 - 7m/5√2 +5=0,

1/25 - 7m/5√2 +5=0,

then

7m/5√2 =1/25 +5,

7m/5√2 =(1+125)/25,

7m/5√2 =126/25,

therefore

m=126/25 × 5√2/7,

m=18/5 ×√2,

m=18√2/5