P(x):x10−3x8+5x6−5x4+3x2−1=0 ∵P(1) and P(−1) are zero ⇒(x−1) and (x+1) are factors. P(x)=(x2−1)(x8−2x6+3x4−2x2+1) Let g(x)=x8−2x6+3x4−2x2+1 =x2(x6−2x4+3x2−2)+1 =x2(x2−1)(x4−x2+2)+1 =x2(x2−1){(x2−
1
2
)2+
7
4
}+1 g(x)≠0 for any real value. ∴ Total number of non-real roots =10−2=8.