18. State the number of positive real zeros, negative real zeros, and complex zeros f(x) = -7x + 10x3 +5x +5 O O or 2 positive real zero O 1 positive real zero O 0 or 4 complex real zero O1 negative real zero 2 complex zeros 0 or 2 negative real zero

Q: Find two positive real numbers x and y such that their product is 800 and x + 2y is as small as…

A: Given that, We have to minimize:

Q: How do we prove a theorem of the form ∀x(P(x)->Q(x))?

A: To prove the theorem of the form ∀x(P(x)→Q(x)), we apply mainly two steps: 1: We take the arbitrary…

Q: To show that ( n + a ) b = θ ( n b ) ( n + a ) b = θ ( n b ) for any real constants a a and b b…

A: Here we use the binomial expansion:

Q: 20. Solve for the Wronskian of the set of functions: 3x - 1, x* - 2. 2x + 3 A. 4x (9x + 10x-90x -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: In Problems 43 and 44, information is given about a complex polynomial f whose coefficients are real…

A: 43. Given degree is 3. Hence there would be at most 3 roots. Given roots are 4+i and 6 Complex roots…

Q: Find all zeros of H(x)=5(x-2)^2(x^2-4x-3). Show work and simplify.

A:

Q: Find 2 positive real numbers x and y such that their sum is 40 and their product is as large as…

A:

Q: Šimplify the complex fraction. 4 + 6-x'x-6 3 3 + x-6 6-x'x-6 xx-6 II 3. 4- 3. 3.

A: Solution: Consider the given complex fraction:…

Q: x2+Kx+64=0 & x2-8x+k=0 w

A: x2+kx+64=0x2-8x+k=0 Take the formula of the discriminant for the real roots, D1,2≥0 where, D=b2-4ac

Q: 14. The condition for the quadratic cquation x2 + 2kx + (k + 6) = 0 to have two uncqual real roots…

A: When a quadratic equation have two real unequal real roots then the value of discriminate is greater…

Q: Show that the real zeros of f(x) = x^4 + 5x^2 + 3x -7 satisfy (a) No real zero is greater than 1.…

A: We have to find the given statement is correct or not.

Q: Find the zeros and give the multiplicity. f(x) = x2(4x + 5)°(x - 6)2 X = (smallest x-value) with…

A:

Q: find the zeros and give the multiplicity  f(x)= (3x+2)^5(x^2-10x+25) x=               (smaller…

A:

Q: Find the zeros and give the multiplicity. f(x) = x2(4x + 5)7(x − 9)2 x =  (smallest x-value)…

A:

Q: Use the Intermediate Value Theorem to show that f(x)=3x^3-x-1 has a zero in the interval [0,1].…

A: Using the intermediate final theorem:f(x)=3x3-x-1, [0,1]First, we are checking the checking the…

Q: A fourth degree polynomial with constant coefficients may have (1) 4 distinct real roots. (1I) 3…

A: Topic:- polynomial

Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: 5. True or False A polynomial function of degree n with real coefficients has exactly n complex…

A: A polynomial function of degree n with real coefficient has exactly n complex zeros. At most n of…

Q: The sum of two positive real numbers x and y is 12. Find an x and y among these such that the…

A: The sum of two positive real numbers x and y is 12.

Q: 3. f(x) = x2- 4x- 5 4. f(x) = X2 - 9x - 36 (x-12)(x+3) roots are x=12 x=-3 5. f(x) = x2+ 3x- 40 6.…

A: Given3)f(x)=x2-4x-55)f(x)=x2+3x-406)f(x)=x2+22x+21 To find Roots of above

Q: 3. Find the complex zeros of f(x) = x – 4x2 + 25x 100.

A: fx=x3-4x2+25x-100=x3-4x2+25x-100=25x-4+x2x-4=x-4x2+25=x-4x+5i(x-5i)

Q: 13. List all possible rational zeros given by the Rational Zeros Theorem for P(x) = 2r +&r+Ilr-14

A:

Q: Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the…

A: To use Descartes's rule of signs to determine the possible number of positive real zeros and the…

Q: 5. What are the real and complex solutions of the polynomial equation 3-8=0 O1+i3, and 1 –i 02, -1…

A: we know that the expansion of       a3-b3=(a-b) (a2+ab+b2) now put the value in it and get

Q: X Y 0 0 1 55 2 110 3 165 wrie a realationship

A: Y= 55X

Q: State the number of complex zeros and the possible number of real and imaginary zeros for the…

A:

Q: 20. Find the rational roots of x +5x+7x-3x-10 0. O-2, 1 O2, 1 O-2, -1 O2, -1 21. Find all the zeroes…

A: For (20), Answer:

Q: Determine between which consecutive integers the real zeros of At) = 3x² – Sx² + Sx + 7 are located…

A:

Q: ) List all the possible rational zeros of flx) = 2r - 5x + 2x + 6 A) 2, ±3, 26 * 21, 2, 23 ±1, C)…

A: Topic = Algebra

Q: 5) Use the Intermediate Theorem and Roll's Theorem show that there is exactly one root of the given…

A:

Q: Find the zeros of f(x), and state the multiplicity of each zero. (Order your answers from smallest…

A: We have to find

Q: Find the zeros of f(x), and state the multiplicity of each zero. (Order your answers from smallest…

A:

Q: a* + 11x + 37x² + 31x – 20, given that x + 5 and a + 4 are Find all the real zeros of f(x) factors…

A: Divide the f(x) by the product of (x+4) and (x+5) and then find the zeroes of the Quotient obtained

Q: Select all quadratics which have real zeroes. O f(2) = (z - 4)² – 2 O f(2) O f(x) = 2x + 4r + 4 - 5a…

A:

Q: 15. What are all the possible rational roots of f(x) = 6x* – x² – 4x² – x – 2? ±1. ±2. ±3, ±6, ±늘,…

A: Rational root problem......

Q: 8. What are the zeros of the FUNction (x +7) (x – 3) (x + 8) O x = 8 There are no zeros X = -7 and 3…

A: Given, x+7x-3x+8  We have to find the zeros of the function.

Q: 23. Simplify the complex fraction કાકાસ x²+2x+3 '' + ; x+3 1 1 -+ x+5

A: Topic = Algebra

Q: Find the zeros and give the multiplicity. f(x) = x2(2x + 3)8(x − 7)2 x =  (smallest x-value)…

A:

Q: The ________ ________ of ________ states that if f(x) is a polynomial of degree n (n > 0), then f…

A: The ________ ________ of ________ states that if f(x) is a polynomial of degree n (n > 0), then f…

Q: Find the cubic polynomial function f(x) with real coefficient that has 2, and 1-i as zero and f(1)=3

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 9. List the Possible Rational Zeros of the function. DO NOT SOLVE! f(x) = 3x3 – 19x2 + 51x + 21

A:

Q: Find the zeros and give the multiplicity. f(x) = x2(3x + 4)6(x − 7)2 x =  (smallest x-value)…

A:

Q: B. Complete the table below: Polynomial Equatlons Degree Real Roots of an Equation Number of Real…

A: 4.x+32x-54x+25=0Degree=11Real roots =-3,5 and -2Number of real roots =11…

Q: 1. Create two different rational polynomial expressions with the following constraints: • one…

A: An expression is undefined when x=4 is given by  px=1xx2-16 An expression is undefined when x=-2 or…

Q: 4. Consider the polynomial f(x) = x* + 1. (a) product of two irreducible quadratics. Explain why ƒ…

A:

Q: 7. Use the Intermediate Value Theorem and the Mean Value Theorem to prove that the equation x – 4x…

A:

Q: Find all the real zeros of f(x) = x* – x² – 24x + 30. Given that f( – 5) = 0. Enter the zero…

A:

Q: Let /(x) – x + 2x+ 3x + 4 € Z). Then x = -1 is a root for /(x) of multiplicity None

A:

Q: Find the zeros and give the multiplicity. f(x) = x2(4x + 5)7(x − 9)2

A: To calculate the zeroes equate the given equation to zero.