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Algebra -4- Cubic Equations II Quantitative Aptitude II CAT 2021 II 16th September

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Question 1

The zeros of the cubic polynomial 2x³ – x² – 2x + 1 are a, b and c respectively. Find a + b + c:

Question 2

; then find the value of x³ −6x² +12x −18.

Question 3

The zeros of a cubic polynomial 2x³ – x² – 2x + 1 are a, b and c respectively. Find (ab+bc+ca).

Question 4

The sum of the cubes of two numbers is 793. The sum of the numbers is 13. Then the difference of the two numbers is:

Question 5

If x = 2 - 2^1/3 + 2^2/3 then the value of x³ - 6x² + 18x + 18 is-

Question 6

(y − z)³+ (z − x)³+ (x − y)³is equal to:

Question 7

If p³ + 3p² + 3p = 7, then the value of p² + 2p is:

Question 8

Find the number of ordered pairs ( x² , y) that satisfy the equation x³ + y³ + 36 xy = 1728, where x and y are positive whole numbers.

Question 9

If the equation x³ – 9x² + 26x – p = 0 has 3 positive real roots, then

Question 10

m is the smallest positive integer such that for any integer n > m, the quantity n³ – 7n² + 11n – 5 is positive. What is the value of m?

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