Let $N$ denote the number that turns up when a fair die is rolled If the probability that the system of equations$ x+y+z=1 $ $ 2 x + Ny +2 z=2 $ $ 3 x +3 y+ N z=3$ has unique solution is $\frac{k}{6}$, then the sum of value of $k$ and all possible values of $N$ is
The correct answer is (C) : 20 x+y+z=1 2x+Ny+2z=2 3x+3y+Nz=3 Δ=∣∣1231N312N∣∣ =(N−2)(N−3)
For unique solution Δ=0
So N=2,3 ⇒P( system has unique solution )=64
So k=4
Therefore sum =4+1+4+5+6=20
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
