Page 43 - CHAPTER 4 (Quadratic equations)

CHAPTER 4
QUADRATIC EQUATIONS

SUBJECTIVE TYPE

23. If the roots of the equation (a +b )x -2(ac+bd)x+(c +d )=0 are equal,
2
2
2
2
2
a
c
prove that = .
b d
24. If p, q, r, s are real numbers such that pr=2(q+s) then show that at
2
least one of the equation x +px+q=0 and x +rx+s=0 has real roots.
2
25. Find the values of x which satisfy the equation

2
2
x -3 x -3
(5+2√6) +(5-2√6) =10.
26. Find the number of integral solutions to the equation (x-2) 25-x 2 =1.
27. If c, d are the roots of x -10ax-11b and a, b are roots of the equation
2

x -10cx-11d, find the value of a+b+c+d.
2
2
28. The coefficient of x in the equation x +px+q=0 was wrongly written
as 17 in place of 13 and the roots thus found were -2 and -15. Find

the roots of the correct equation.

29. If a gym charges its members Rs 300 per year to join, they get 1000

members. For each Rs 2 increase in price they can expect to lose 5

members. How much should the gym charge to maximize its

revenue? What is the gym's maximum revenue?

30. There is a two digit number given whose digits are the same and

has got the following property : When squared, it produces a four-

digit number, whose first two digits are the same and equal to the

original's minus one, and whose last two digits are the same and

equal to the half of the original's. Find that number.

43