CA Foundation · Quantitative Aptitude · Equations
If α and β are the roots of the equation 2x² − 10x + 6 = 0, what is the value of α + β + αβ?
The sum of the roots is 5 and the product is 3, so α+β+αβ equals 8. For ax²+bx+c, the sum is −b/a, which is 10/2, and the product is c/a, which is 6/2. Adding the two values gives the required result.
- A8Correct
- B2
- C13
- D−2
Explanation
For ax² + bx + c = 0, the sum of roots is −b/a = 10/2 = 5 and the product is c/a = 6/2 = 3. So α + β + αβ = 5 + 3 = 8. The value 2 comes from subtracting the product from the sum, which is not what is asked.
Did you get it right without looking?
One question tells you little. A timed set on Equations shows your real accuracy, how long you take and where you lose marks.
More Equations questions
- Meera borrowed ₹50,000 at a compound interest rate. After 2 years, she owes ₹60,500. If the interest is compounded annually, what is the rat…
- For what positive value of k does the equation x² + kx + 16 = 0 have two equal roots?
- A company's profit function is represented by P(x) = −2x² + 40x − 150, where x is the number of units produced (in hundreds). At what produc…
- The length of a rectangular plot is 5 metres more than its breadth, and its area is 336 square metres. What is the perimeter of the plot?
- For what value of k does the equation kx² − 12x + 9 = 0 have two equal real roots?
- Ravi invests ₹x at a simple interest rate of 6% per annum and ₹(10,000 − x) at 8% per annum. His total annual interest is ₹700. What is the …