Question

Solution

Correct option is

At least one irrational root

Putting ax = y (1) can be written as

y3 + by2 + acy + a2d = 0         ... (2)

If (1) has all rational roots then (2) has all integral roots. If α, β, γ are roots of (2) then α, β, γ are divisors of a2 d and as such must be odd integers. Now

– b = α + β + γ ⇔ b is odd

and               ac = βγ + γα + αβ ⇔ c is odd

⇒                bc is odd. A contradiction.

SIMILAR QUESTIONS

Q1

A bag contains 2 Black, 4 white and 3 Red balls. One ball is drawn at random and kept aside. Then another ball is drawn and is also kept aside. This process is continued till all are drawn. Find the probability that the balls drawn are in the sequence 2 Black, 4 white and 3Red

Q2

If X follows a binomial distribution with parameters n = 100, p = 1/3, then P(X = r) is maximum when r =

Q3

A team of 8 couples, (husband and wife) attend a lucky draw in which 4 persons picked up for a prize. Then, the probability that there is at least one couple is

Q4

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is

Q5

If X following a binomial distribution with parameters n = 8 and p = 1/2, then equals

Q6

Two numbers b and c are chosen at random with replacement from the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9. The probability that x2 + bx + c > 0 for all x Ïµ R is

Q7

India plays two matches each with west indies and Australia. In any one match, the probabilities of India getting points 0, 1, 2 are respectively 0.45, 0.05 and 0.05 and 0.50 for base drawn and won. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

Q8

If two events A and B are such that P(AC) = 0.3, P(B) = 0.4 and P(ABC) = 0.5 then P(B/A  BC) =

Q9

A bag contains n + 1 coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is 7/12, then the value of n is