3. Let a and b be positive real numbers. Let 3 3 f (x) = a(x + 2x2 – 1) + b(x³ + x – 2). - Show that f(x) has at least one real number c such that f(c) = 0. Hint: Consider the zeroes of the polynomials x3 + 2x2 –1 and r3 + x – 2. -

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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plz do it through intermediate value theorem as solved in sample ques

3. Let a and b be positive real numbers. Let
3
3
f (x) = a(x + 2x2 – 1) + b(x³ + x – 2).
-
Show that f(x) has at least one real number c such that f(c) = 0.
Hint: Consider the zeroes of the polynomials r3 + 2x2 – 1 and r3
-
Transcribed Image Text:3. Let a and b be positive real numbers. Let 3 3 f (x) = a(x + 2x2 – 1) + b(x³ + x – 2). - Show that f(x) has at least one real number c such that f(c) = 0. Hint: Consider the zeroes of the polynomials r3 + 2x2 – 1 and r3 -
SEMESTER I, 221/2022
Tutorial 2, Problem 8
Suppose b>a
Show that the function
F(r) = (z - a) (z - b) +=
takes on the value (a + b)/2 for some value z.
FLA is
on R sie it a polynomial.
continuous
Fla)= a
Sine tb <b by intermedinte value
theorem there enist CE[a, b] such that
Transcribed Image Text:SEMESTER I, 221/2022 Tutorial 2, Problem 8 Suppose b>a Show that the function F(r) = (z - a) (z - b) += takes on the value (a + b)/2 for some value z. FLA is on R sie it a polynomial. continuous Fla)= a Sine tb <b by intermedinte value theorem there enist CE[a, b] such that
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