# CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

###### CAT Questions | Algebra | Polynomials - Polynomial Remainder Theorem CAT Questions

The question is about Polynomial Remainder Theorem. We need to find out the range which is also a solution to the given inequality. This question is one of the tougher examples of remainder theorem but it can be solved nonetheless. Check it out! Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions.

Question 2: Solve the inequality x3 – 5x2 + 8x – 4 > 0.

1. (2,$$infty \\$) 2.$1, 2) $$cup\\$$2, $$infty\\$) 3.$-$$infty \\$, 1) $\cup\\$$2, $$infty \\$) 4.$-$$infty \\$, 1) ## Nail CAT 2020 with Test Dojo2,500 off on Dojo and Part courses. Signup Now! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Online Batches Available Now! ### Explanatory Answer ##### Method of solving this CAT Question from CAT Algebra - Polynomials: This question is one of the tougher examples of remainder theorem but it can be solved nonetheless. Check it out!! Let a, b, c be the roots of this cubic equation a + b + c = 5 ab + bc + ca = 8 abc = 4 This happens when a = 1, b = 2 and c = 2 {This is another approach to solving cubic equations.} The other approach is to use polynomial remainder theorem. If you notice, sum of the coefficients = 0 => P$1) = 0
=> (x – 1) is a factor of the equation. Once we find one factor, we can find the other two by dividing the polynomial by (x–1) and then factorising the resulting quadratic equation.
(x – 1) (x – 2) (x – 2) > 0

Let us call the product (x – 1)(x – 2)(x – 2) a black box.
If x is less than 1, the black box is a –ve number.
If x is between 1 and 2, the black box is a +ve number.
If x is greater than 2, the black box is a +ve number.
Since we are searching for the regions where black box is a +ve number, the solution is as follows:

1 < x < 2 OR x > 2

The question is "Solve the inequality x3 – 5x2 + 8x – 4 > 0."

##### Hence the answer is "(1, 2) $$cup\\$$2, $$infty\\$)" Choice B is the correct answer. ###### Nail CAT 2020 with 2IIM. 2,500 Off on Test Dojo and Part courses. Signup Now ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 30,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiPrices slashed by Rs 5000/- Attend a Demo Class ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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