CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

CAT Questions | Algebra | Polynomials - Polynomial Remainder Theorem

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) Best CAT Online Coaching Try upto 40 hours for free Learn from the best! 2IIM : Best Online CAT Coaching. Best CAT Coaching in Chennai CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register 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. Best CAT Online Coaching Try upto 40 hours for free Learn from the best! Already have an Account? CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar Best CAT Coaching in Chennai Attend a Demo Class Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! 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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