Asked by Emily
For our homework we had to read this one section which demonstrated the location principle (just in case this has a different name, I'll post it here:)
"If P(x) is a polynomial with real coefficients and a and b are real numbers such that P(a) and P(b) have opposite signs, then between a and b there is at least one real root r of the equation P(x)=0."
I definitely do NOT understand what the heck this means. Can someone please explain it, along with an example maybe? Any help is greatly appreciated, thanks!!
"If P(x) is a polynomial with real coefficients and a and b are real numbers such that P(a) and P(b) have opposite signs, then between a and b there is at least one real root r of the equation P(x)=0."
I definitely do NOT understand what the heck this means. Can someone please explain it, along with an example maybe? Any help is greatly appreciated, thanks!!
Answers
Answered by
drwls
Do you know what a polynomial with real coefficients is?
It is a formula that is the sum of integer powers of x with constant real coefficients, plus a constant term. That is what they are calling P(x).
If there are two values a and b which, when substituted for x, result in P(a) and P(b) being of opposite signs, then there is at least one value of x between a and b for which P(x) = 0
It is a formula that is the sum of integer powers of x with constant real coefficients, plus a constant term. That is what they are calling P(x).
If there are two values a and b which, when substituted for x, result in P(a) and P(b) being of opposite signs, then there is at least one value of x between a and b for which P(x) = 0
Answered by
Darryl
Tammy mixes the letters S, C, H, O, O, and L thoroughly. Without looking, Allen draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that Allen will not select a consonant?
Tammy mixes the letters S, C, H, O, O, and L thoroughly. Without looking, Allen draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that Allen will not select a consonant?
Tammy mixes the letters S, C, H, O, O, and L thoroughly. Without looking, Allen draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that Allen will not select a consonant?
Tammy mixes the letters S, C, H, O, O, and L thoroughly. Without looking, Allen draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that Allen will not select a consonant?
Tammy mixes the letters S, C, H, O, O, and L thoroughly. Without looking, Allen draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that Allen will not select a consonant?
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