Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

According to Descartes' Rule of Signs, can the polynomial function have exactly 11 positive real zero, including any repeated zeros? Choose your answer based on the rule only.\newlinef(x)=x4+5x3+2x2−4x−5f(x) = x^4 + 5x^3 + 2x^2 - 4x - 5\newlineChoices:\newline(A)yes\newline(B)no

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Descartes' Rule of Signsright chevron icon

Full solution

Q. According to Descartes' Rule of Signs, can the polynomial function have exactly 11 positive real zero, including any repeated zeros? Choose your answer based on the rule only.\newlinef(x)=x4+5x3+2x2−4x−5f(x) = x^4 + 5x^3 + 2x^2 - 4x - 5\newlineChoices:\newline(A)yes\newline(B)no
  1. Count Sign Changes: Count the number of sign changes in the coefficients of f(x)=x4+5x3+2x2−4x−5f(x) = x^4 + 5x^3 + 2x^2 - 4x - 5. Coefficients: 1,5,2,−4,−51, 5, 2, -4, -5. Sign changes: 11 (from 22 to −4-4).
  2. Descartes' Rule: According to Descartes' Rule of Signs, the number of positive real zeros is equal to the number of sign changes or less by an even number.\newlineSince we have 11 sign change, f(x)f(x) can have either 11 or 00 positive real zeros.
  3. Determine Positive Zero: Determine if f(x)f(x) can have exactly 11 positive real zero.\newlineSince the possible number of positive real zeros is 11 or 00, it is possible for f(x)f(x) to have exactly 11 positive real zero.

More problems from Descartes' Rule of Signs

Question
Find the degree of this polynomial.\newline`5b^{10} + 3b^3`\newline_______
Get tutor helpright-arrow

Posted 5 months ago

Question
Subtract.\newline(9a+5)−(2a+4)(9a + 5) - (2a + 4)\newline____
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the product. Simplify your answer. \newline−3v2(v2−9)-3v^2(v^2 - 9)\newline________
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the product. Simplify your answer.\newline(v−3)(4v+1)(v - 3)(4v + 1)\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the square. Simplify your answer.\newline(3y+2)2(3y + 2)^2\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Divide. If there is a remainder, include it as a simplified fraction.\newline(24t2+36t)÷6t(24t^2 + 36t) \div 6t\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Is the function q(x)=x6−9 q(x) = x^6 - 9 even, odd, or neither?\newlineChoices:\newline[[even][odd][neither]]\text{[[even][odd][neither]]}
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the product. Simplify your answer. \newline−3q2(−3q2+q)-3q^2(-3q^2 + q)\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the product. Simplify your answer.\newline(r+3)(4r+2)(r + 3)(4r + 2)\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the roots of the factored polynomial.\newline(x+7)(x+4)(x + 7)(x + 4)\newlineWrite your answer as a list of values separated by commas.\newlinex=x = ____
Get tutor helpright-arrow

Posted 9 months ago

View all (26)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant