Mathematics
Determine whether the following quadratic equation has real roots.
5š„2 ā 9š„ + 4 = 0
(a) Give reasons for your answer.
(b) If the equation has real roots, identify them.
Related Questions
Aman has 500, ā¹ 100 shares of a company quoted at ā¹ 120, paying a 10% dividend. When the share price rises to ā¹ 200 each, he sells all his shares. He invests half of the sale proceeds in ā¹ 10, 12% shares at ā¹ 25, and the remaining sale proceeds in ā¹ 400, 9% shares at ā¹ 500.
Find his:
(a) sales proceeds.
(b) investment in ā¹ 10, 12% shares at ā¹ 25.
(c) original income.
(d) change in income.
The profit in rupees in a local restaurant and the number of customers who visited the restaurant are tabulated below for each week for one month.
Week number Week 1 Week 2 Week 3 Week 4 Number of customers 1400 5600 x 3212 Profit in ā¹ 28000 112000 32140 y Find :
(a) if the number of customers and profit per week in continued proportion or not? Justify your answer.
(b) the value of x and y.
Given, 9š„2 - 4 is a factor of 9š„3 - mš„2 - nš„ + 8 :
(a) find the value of m and n using the remainder and factor theorem.
(b) factorise the given polynomial completely.