For the equation x8+6x7−5x4−3x2+2x−5=0, determine the maximum number of real roots possible.
Options:
A . 4
B . 3
C . 8
D . 7
E . Can’t be determined
Answer: Option A : A f(x)=x8+6x7−5x4−3x2+2x−5 Check the number of positive roots= no. of sign changes in f(x) = 3 Check the number of negative roots = no. of sign changes in f(-x) f(−x)=x8−6x7−5x4−3x2−2x−5. No. of sign changes = 1 Now check for zero as a root.f(0)=−5≠0 So, maximum number of real roots = 3 + 1 = 4. Hence option (a)
