Question
I. 2p2 + 5p + 2 = 0Â Â Â Â Â Â Â Â II.
2q2 + 11 q + 14 = 0 In each question two equations are provided. On the basis of these you have to find out the relation between p and q. Give answer.Solution
I. 2p2 + 5p + 2 = 0  (2p + 1) (p + 2) = 0  p = - (1/2) or -2  II. 2q2 + 11 q + 14 = 0  (q + 2) (2q + 7) = 0  q = -2 or - (7 /2)  Hence, p ≥ q  Alternate Method:  if signs of quadratic equation is +ve and +ve respectively then the roots of equation will be -ve and -ve. So, roots of first equation = p = -1/2, -2 if signs of quadratic equation is +ve and +ve respectively then the roots of equation will be -ve and -ve. So, roots of second equation = q = -2, -7/2 After comparing roots of quadratic eqution we can conclude that p ≥ q.
The average age of a group of five friends is 78 years. If a friend, aged 48 years, is replaced by another friend, then the avera...
? = 234.87 + 32.14% of (59.88 x 70.04)
The difference between the lengths of two parallel sides of a trapezium is 12 cm. The perpendicular distance between these two parallel sides is 60 cm. ...
In a 240 ml mixture containing milk and honey, honey makes up 56.25% of the total mixture. After removing 'p' ml of this mixture, 8 ml of honey is added...
"M' sold a watch to 'N' making a profit of 20%. 'N' then sold it to 'X' at a 10% loss. If 'M' had directly sold the watch to 'X' ...
A coin is tossed. If head occurs, a ball is drawn from a bag containing 3 red and 4 green balls. If tail occurs, a die is thrown. The probability that t...
A cube of volume 768 cm³ is molded into a cuboid whose length, width, and height are in the ratio 2: 2: 3. Find the length of the cuboid.
If A and B are both symmetric matrices of the same order, then which of the following is necessarily skew-symmetric?
A group of 30 students has an average score of 60 in an exam. If 5 more students join the group and their average score is 70, find the new average scor...
In triangle ABC, if angle A = 30°, angle B = 60°, and side a = 10 cm, find side b.
