If f(a) = 4x3 - 11x + 14x - 6, then show the values f(0) and f(1) have different algebraic signs.Explain why this information along with the fact that a polynomial function is continuous everywhere enables us to conclude that f has a zero in the interval [0, 1] %3D

Q: Show that f(x) = 2/x2 + 3x4 – 5x6 is an even function

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Q: Show that f(x) = x4 + 4.x + c has at most two real roots for any umber c.

A: Consider the given equation. fx=x4+4x+c Case 1: When c>0. No sign change, by Descartes rule of…

Q: = x? – 5x + 7 has roots a and B. Use symmetric Suppose that f(x) functions to find a + B, aß, a² +…

A: If we have a quadratic equation ax2+bx+c=0 and α and β are the roots then: α+β=-ba αβ=ca We can use…

Q: Is f (x) = x2 + 2 one-to-one? If not, describe a domain on which it is one-to-one.

A: Given that the function is f (x) = x2 + 2   f(2)=22+2=6 f(-2)=(-2)2+2=6 So, f(2)=f(-2) So for two…

Q: A function f is defined by Ax + 5 f(x) 6x - 2 If f(1) = 4, find A.

A: Given: fx=Ax+56x-2  ……1   and, f1=4  ……2   To find: A

Q: Show that the function g(x) = x³ – 7x² + 25x + 8 has exactly one real root- |

A: Given: gx=x3-7x2+25x+8 To show function gx has exactly one real root.

Q: Please determine the domain of the function

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Q: 8. Find one zero of the polynomial f(x)=2x-x-6x+3 %3D

A: Given function is: Apply rational root theorem to get roots of polynomial. If the polynomial has a…

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.