Matrices question
Matrix M= [a k ]
[ 1 a-k] it's a 2 by 2 matrix
We are given that detM > 0 for all values of a and we need to find the range of possible values of k. I have already found the equation for the detM which is a^2-ak-k and I know the next step is to find the discriminant to find the value of k. However, I don't understand why it is b^2-4ac< 0 instead of b^2-4ac >0. Thank you!
[ 1 a-k] it's a 2 by 2 matrix
We are given that detM > 0 for all values of a and we need to find the range of possible values of k. I have already found the equation for the detM which is a^2-ak-k and I know the next step is to find the discriminant to find the value of k. However, I don't understand why it is b^2-4ac< 0 instead of b^2-4ac >0. Thank you!
(edited 12 months ago)
Original post by GLUM
Matrix M= [a k ]
[ 1 a-k] it's a 2 by 2 matrix
We are given that detM > 0 for all values of a and we need to find the range of possible values of k. I have already found the equation for the detM which is a^2-ak-k and I know the next step is to find the discriminant to find the value of k. However, I don't understand why it is b^2-4ac< 0 instead of b^2-4ac >0. Thank you!
[ 1 a-k] it's a 2 by 2 matrix
We are given that detM > 0 for all values of a and we need to find the range of possible values of k. I have already found the equation for the detM which is a^2-ak-k and I know the next step is to find the discriminant to find the value of k. However, I don't understand why it is b^2-4ac< 0 instead of b^2-4ac >0. Thank you!
If your quadratic is always positive (or always negative), it has no roots, so the discriminant must be negative - the quadratic doesn't touch or cross the x-axis (or in this case the a-axis).
(edited 12 months ago)
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