The other two roots are imaginary, viz. (-3+4.58i) and (-3-4.58i)

You can ignore those values.

For x=5, since the function becomes 0, (x-5) is one of the roots. Then divide the function by (x-5) to get remaining roots.

You can further factorize x^2+6x+30 and get the imaginary of roots.

]]>For thousands place, the digit can be anything but 0. So total 9 possibility.

For hundreds place, any of the 10 digits can be present, except the thousands-digit number. So 9 possibility again.

For tens place, any of the 10 digits except the two digits used above. So 8 possibilities.

Lastly, for ones place, any of the 10 digits except the three used already. So 7 possibilities.

This, the total number of 4-digit number with no digit repeated = 9 x 9 x 8 x 7 = 4536

]]>Conclusion:

(U1+U2), (U1*U2), U1^2 & (L1+L2) are always Triangular Matrices (first 3 matrices – Upper Triangular & last matrix – Lower Triangular) if all of these operations can be done.

(U1+L1) & U1L1 can be a triangular matrix only if both U1 & L1 are diagonal matrices (i.e. both upper & lower triangular matrices) of the same order. Otherwise, they are not triangular matrices.

]]>The solution is attached below… ]]>

The solution is attached below… ]]>

= 4x – 12 – ax + 2x – 3

= (6 – a)x – 15 ]]>

The function is f(x) = x * (x+1)

For x = 9, f(x) = 9*10 = 90

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