Show that ` A=[[-8,5],[2,4]]` satifies the equation ` x^2 +4x-42=0 `

Find the inverse of each of the matrices given below : Show that the matrix A=[(-8,5),(2,4)] satisfies the equation A^(2)+4A-42I=0 and hence find A^(-1) .

Solve the equation 4^(x)- 5 xx2^(x) + 4 = 0.

If the arithmetic mean and geometric mean of the p^(th) and q^(th) terms of the sequence -16,8,-4,2,… satisfy the equation 4x^2-9x+5=0 , then p+q is equal to "______"

The sum of the values of X satisfying the equation |x^(2)+4x+3|+2x+5=0 is :

Let a=(pi)/(7) , then (a) show that sin^(2)3a-sin^(2)a=sin2asin3a (b) show that co sec a=co sec 2a+co sec4a . (c) Prove that cos a is a root of the equation 8x^(3)+4x^(2)-4x+1=0 .

Prove that sinfrac {pi}{14} is a root of the equation 8x^(3) -4x^(2) - 4x +1 = 0 .

The sum of the roots of the equation 4^(x) - 5.2^(x) +4=0 is

The order of the multiple roots of 2 of the equation x^(4)-5x^(3)+6x^(2)+4x-8=0 is