Find the value of k, if the sum of the square of the roots of x² - 3kx + 4k² = 0 is equal to ______?
Answer: ±1
Explanation
Given equation: x^2 - 3kx + 4k^2 = 0.
Sum of roots = 3k, Product of roots = 4k^2.
Sum of squares of roots = (sum of roots)^2 - 2(product of roots)
= (3k)^2 - 2(4k^2)
= 9k^2 - 8k^2
= k^2.
Given sum of squares = one of the options.
If sum of squares = 1, then k^2 = 1, so k = ±1
This question appeared in
Past Papers (5 times)
ETEA 25 Years Past Papers Subject Wise (Solved) (2 times)
ETEA Past Papers (1 times)
KPK Teacher Past Papers SST PST CT TT PET (2 times)
This question appeared in
Subjects (1 times)
MATHS MCQS (1 times)
Related MCQs
- Find the value of k so that the sum of the roots of the equation 2x² + kx + 6 = 0 is equal to four times the product of its roots?
- Find the value of n if both sum and product of roots of the quadratic equation mx² - 5x + n = 0 are equal to 10?
- The base and altitude of the parallelogram is 16 cm and 9 cm. If the area of a square is equal to the area of this parallelogram, find the length of the side of the square?
- Find the quadratic equations whose roots are the reciprocals of the roots of 2x^2 + 5x + 3 = 0?
- 1 square foot is equal to ______?
- A cube has ______ equal square faces.
- 1 square foot is equal to how many square meters?
- One square meter is equal to how many square feet?
- One Square foot is equal to 144sq inches and one meter is equal to?
- A square field whose one side lenth is 5 cm. Find the area of a square?
