Question
If the sum of the squares of the roots of p2
- (x-2)p - (x+1) = 0 is 5 then what is the value of x.Solution
Let the roots of equation be a and b. Given that, a2 + b2 = 5 We know that, (a+b )2 = a2 + b2 + 2ab Or, (a+b )2 – 2ab = a2 + b2 Sum of roots = -(-(x-2)), product of roots = -(x + 1) (x – 2)2 – 2 × 1 × – (x+1) = 5 Or, x2 + 4 – 4x + 2x + 2 = 5 Or, x2 – 2x + 1 = 0 Or, (p – 1)2 = 0 Or, p = 1
Meena invested Rs. 10,500 at 30% p.a. for 2 years and Rs. 7,200 at 28% p.a. for 4 years on simple interest. How much interest did she receive in total?
A certain amount of money, when invested at an annual compound interest rate of 'x%' compounded annually, grows to 1.5376 times its original value in 2 ...
What sum of money must be given at simple interest for 5 months at 3% per annum in order to earn Rs. 260 interest?
An amount of Rs. 3,000 is invested for 2 years at a compound interest rate of 10% per annum. The interest gained is used to buy an item. If the item is ...
An individual invests ₹1,200 at a simple interest rate of 5% per annum. After 2 years, they add ₹800 to the investment, and the total amount remains...
The simple interest on a sum of Rs X in 5 years is 2/5 of the principal. What is the annual rate of interest?
A person 'P' invested Rs. 800 for 2 years at an interest rate of 'a'% per annum, Rs. 450 for 4 years at an interest rate of (a - ...
Vipul invested Rs.4000 at the rate of R% simple interest for four years and he got Rs.1600 as interest. If he invest same amount for 2 years in C.I. an...
Rs.700 amounts to Rs.742 in 2 years at a certain rate. If interest rate is increased by 2%, then what will be the new interest?
Simple interest and compound interest (compounded annually) earned on a sum at the end of 2 years at a certain rate of interest p.a. are Rs. 1100 and Rs...
Relevant for Exams:
