Find the matrix of the quadratic form. Assume x is in set of real numbers R-squared.(a) 2x₁² + 12 x₁x₂ - 5x₂²(b) 6x₁x₂

The matrix is:

(26)

(6-5)

Step-by-step explanation:

The coefficient of the squared terms (2 and -5) are written in the diagonal, and the coefficient of x₁x₂ (12) is split equally in each column.

The matrix is:

(26)

(6-5)

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

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step-by-step explanation:

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