Question: If $x,\mspace{6mu} y,\mspace{6mu} z$, then the roots of the equation \(u = x^{2} + 4y^{2} + 9z^{2...

Question

If $x,\mspace{6mu} y,\mspace{6mu} z$ , then the roots of the equation

$u = x^{2} + 4y^{2} + 9z^{2} - 6yz - 3zx - zxy$ are.

Answer 1

We have $a \in \lbrack 2,8\rbrack$ Let roots are $a \in \lbrack - 2,8\rbrack$ and $a \in (2,8)$

Let $a \in ( - 2,8)p,q \in \{ 1,2,3,4\}$

Given that, $px^{2} + qx + 1 = 0$

Putting this value, we get

$x^{2} - (3k - 1)x +$ .

Hence roots are real.

Question: If \(x,\mspace{6mu} y,\mspace{6mu} z\), then the roots of the equation \(u = x^{2} + 4y^{2} + 9z^{2...