Question

If one root of the equation\(\Large{x^2-12x+3k=0}\) is the square of the other the value of \(\Large{k}\) is:-

Answer 1

If \(s\) and \(s^2\) are the roots then the product of roots is \(s^3\). And the product is given by \(3k\).

Answer 2

I did this as follows:- \[\text{Ist root}= \frac{12 + \sqrt{144-12k}}{2}\]\[\text{IInd root} = \frac{12-\sqrt{144-12k}}{2}\] since larger root is the square of smaller. therefore,\[\text{Ist root}=\left( 12-\sqrt{144-12k}\over2 \right)^2\]\[\left( 12-\sqrt{144-12k}\over2 \right)^2={12+\sqrt{144-12k}\over2}\]

Answer 3

The sum of roots is \(12\) so I can just guess that the roots are \(3\) and \(9\).

Answer 4

So \(3k = 3\times 9\)

Answer 5

Ans hi 9 hai

Answer 6

Haan because \(3k=3\cdot 9 \iff k = 9\)

Answer 7

accha to mujhe pura thik tarke se samjho ki tumne kaise kiya

Answer 8

samjhao*

Answer 9

Main samjhata hoon.
\(s\) and \(s^2\) are the roots, right?

Answer 10

right

Answer 11

Vieta's formula ab dekho. \(s^2 + s = 12\) (sum of roots). Toh\[s(s + 1) = 12 \iff s = 3 \iff s^2 = 9\]

Answer 12

Haan. Samajh gaye?

Answer 13

haan thike samajh aa gya

Answer 14

Thaanx!

Answer 15

=)