Quadratic EquationHard
Question
Let $M = 3x^{2} - 8xy + 9y^{2} - 4x + 6y + 13$, where $x,y \in R$, then
Options
A.M can not be equal to zero
B.M must be negative
C.$M > 2$
D.M must be positive
Solution
$M = 3x^{2} - 8yx + 9y^{2} - 4x + 6y + 15$
$$\begin{matrix} & \ = 2\left( x^{2} - 4xy + 4y^{2} \right) + \left( y^{2} + 6y + 9 \right) + \left( x^{2} - 4x + 4 \right) + 2 \\ & \ = 2(x - 2y)^{2} + (y + 3)^{2} + (x - 2)^{2} + 2 \\ & \ \Rightarrow \ M > 2 \end{matrix}$$
Create a free account to view solution
View Solution FreeMore Quadratic Equation Questions
The equation has...The HM of the roots of the equation x2 − 8x + 4 = 0 is -...Let $\alpha$ and $\beta$ be the roots of equation $x^{2} + 2ax + (3a + 10) = 0$ such that $\alpha < 1 < \beta$. Th...The number of values of k, for which the system of equations :(k + 1)x + 8y = 4kkx + (k + 3)y = 3k - 1has no solution, i...If α and β are roots of ax2 − bx + c = 0, then (α + 1) (β + 1) is equal to -...