Write the quadration the arithmetic and geometric means of whose … - Vidyadip

Question

Write the quadration the arithmetic and geometric means of whose roots are A and G respectively.

✓

Answer

Let $\alpha,\beta, $ be roots of equation, so equation is
$\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta=0$
Here,
$\frac{\alpha+\beta}{2}=\text{A}$
$\alpha+\beta=2\text{A}$
And $\sqrt{\alpha\beta}=\text{G}$
$\alpha\beta=\text{G}^2$
So, Required equation is,
$\text{x}^2-2\text{Ax}+\text{G}^2=0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "1 Marks Question" from Geometric Progressions→Geometric Progressions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Which of the following statements are true and which are false? In each case give a valid reason for saying so:
q: The centre of a circle bisects each chord of the circle.

Write down the all possible subset of the given set.
{0, 1}

Write the following statements in the form "if p, then q".
Whenever it rains it is cold.

Given pair of sets are disjoint? {a, e, i, o, u} and {c, d, e, f}

A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space for this experiment.

Taking the set of natural numbesrs as the universal set, write down the complement of the set: {x : x is a perfect cube}

Let a sample space be S = {$\omega_1, \omega_2,..., \omega_6$}.Which of the following assignments of probabilities to each outcome are valid?

Outcomes	$\omega_1$	$\omega_2$	$\omega_3$	$\omega_4$	$\omega_5$	$\omega_6$
	$\frac 1{12}$	$\frac 1{12}$	$\frac 16$	$\frac 16$	$\frac 16$	$\frac 32$

Express the complex numbers i⁹ + i¹⁹ in the form a + ib.

Given that N = {1, 2, 3, ..... , 100}. Then write.
The subset of N whose element are perfect square numbers.

If E and E₂ are independent evens, write the value of $\text{p}\Big(\big(\text{E}_1\cup\text{E}_2\big)\cap\Big(\overline{\text{E}}\cap\overline{\text{E}}_2\Big)\Big).$