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Cubic equations || Quantitative Aptitude || CAT 2021 || 13 May
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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
The zeros of a cubic polynomial 2x3 – x2 – 2x + 1 are a, b and c respectively. Find (ab+bc+ca).
Question 3
If x−2 is a common factor of x3 − 4x2 + ax + b and x3 − ax2 + bx + 8; then find the values of a and b, respectively?
Question 4
If x = 2 - 21/3 + 22/3 then the value of x3 - 6x2 + 18x + 18 is-
Question 5
(y − z)3 + (z − x)3 + (x − y)3 is equal to:
Question 6
What will be the remainder, when 3x3 + x2 + 5x + 8 is divided by 1 + 2x + x2?
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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