Question
If ‘y1’ and ‘y2’ are the roots of quadratic
equation 5y2 – 25y + 15 = 0, then find the quadratic equation whose roots are ‘3y1’ and ‘3y2’.Solution
For an equation of the form ax2 + bx + c = 0, Sum of roots = (-b/a) Product of roots = (c/a) Sum of roots (y1 + y2) = – (–25/5) = –(–5) = 5 Product of roots (y1 × y2) = (15/5) = 3 Sum of roots of required equation = 3y1 + 3y2 = 3 × (y1 + y2) = 3 × 5 = 15 Product of roots of required equation = 3y1 × 3y2 = 9 × y1 × y2 = 9 × 3 = 27 Quadratic equation is: y2 – (sum of roots) × y + (product of roots). So, required equation = y2 – 15y + 27 = 0
- Nisha deposits Rs. 'z' and Rs. (z + 1000) in two accounts for 1 year each. The first earns 11% and the second 9% simple interest. If the total interest fro...
The difference between the compound interest, compounded annually and simple interest on Rs. ‘P’ at the rate of 20% p.a. for 2 years, is Rs....
On Rs. 6000 invested at a simple interest at the rate of 4% p.a., Rs. 2400 is obtained as interest in certain years. In order to earn Rs. 4800 as intere...
Anjali invested Rs.6000 in a scheme offering compound interest of x% p.a. compounded annually. If at the end of 2 years, interest received by her from t...
The difference between the simple interest and the compound interest compounded annually at the same rate on a sum of money at the end of two years is R...
- A person invested Rs. 45,000 in two different schemes together. One scheme offers a simple interest of 9% p.a., while the other scheme offers a simple inte...
A sum of money grows to Rs. 1560 when invested at a simple interest rate of 15% per annum for 2 years. What will be the total amount received if the sa...
Simple interest received at the rate of 12% p.a. for 10 years on a principal amount of Rs. 3600 is twice of the simple interest received at 10% p.a. for...
- The simple interest earned on a certain sum at 12% per annum for 6 years is equal to 2/5 of the compound interest earned on ₹10,000 at 15% per annum, com...
Simran Funded Rs. 70,000 in two different SIP's. She funded the smaller amount at CI of 20% p.a. compounded annually, and larger amount at SI of 16.5% f...
