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