Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation - Mathematics MCQ AIEEE 2004 2004 | ExamTest.live | ExamTest.live

Home Tests Search Rank Profile

easyMCQAIEEE 20042004Mathematics

1 attempts0% success rate3 marks (−1)

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

A $x^{2} + 18 x + 16 = 0$
B $x^{2} - 18 x - 16 = 0$
C $x^{2} + 18 x - 16 = 0$
D $x^{2} - 18 x + 16 = 0$

Solution & Step-by-step Explanation

Let the two numbers be a and b . Arithmetic Mean (AM) = \frac{a + b}{2} = 9 \Rightarrow a + b = 18 . Geometric Mean (GM) = ab = 4 \Rightarrow ab = 16 . A quadratic equation with roots a and b is given by: x^{2} - (Sum of roots) x + (Product of roots) = 0 x^{2} - (a + b) x + ab = 0 . Substituting the values: x^{2} - 18 x + 16 = 0 .

Practice this question

Try it yourself before checking the explanation above.

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

A

x^{2} + 18 x + 16 = 0

B

x^{2} - 18 x - 16 = 0

C

x^{2} + 18 x - 16 = 0

D

x^{2} - 18 x + 16 = 0

Share This Question

quadratic equations progression

Related Questions

Let R=\(1,3), (4, 2), (2, 4), (2, 3), (3, 1)\ be a relation on the set A=\1,2,3,4\. The relation R is

The graph of the function y=f(x) is symmetrical about the line x=2 then

Let A=0&0&-1\\ 0&-1&0\\ -1&0&0. The only correct statement about the matrix A is

If 2a+3b+6c=0, then at least one root of the equation ax^2+bx+c=0 lies in the interval

Let α, β be such that π<α-β<3π. If α+β=-21/65 and α+β=-27/65, then the value of α-β/2 is

The sum of the first n terms of the series 1^2+2×2^2+3^2+2×4^2+5^2+2×6^2+... is (n+1)^22 when n is even. When n is odd the sum is

Ready for a Full Test?

Practice with timed mock tests and track your performance across Mathematics.

Browse Tests Leaderboard

Discussion