Question
For the equation x8+6x7−5x4−3x2+2x−5=0, determine the maximum number of real roots possible.
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)
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:
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)
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