`7x_(1)-x^(2)-x_(3)=0`
`10x_(1)-2x_(2)+x_(3)=0`
`6x_(1)+x_(2)-2x_(3)=7`

Solve x_(1)+2x_(2)+3x_(3)=4 4x_(1)+5x_(2)+6x_(3)=7 7x_(1)+8x_(2)+9x_(3)=10

If |{:(x^(2) +x , 3x - 1 , -x + 3),(2x +1 , 2 + x^(2) , x^(3) - 3),(x - 3, x^(2) + 4, 3x):}| = a_(0) + a_(1) x + a_(2) x^(2) + .... + x_(7) x^(7), then the value of a_(0) is

The minimum value of z=2x_(1)+3x_(2) subjected to the constraints 2x_(1)+7x_(2)ge22,x_(1)+x_(2)ge6,5x_(1)+x_(2)ge10 and x_(1),x_(2)ge0 , is

The minimum value of z=2x_(1)+3x_2 subjected to the constraints 2x_(1)+7x_(2)ge22,x_(1)+x_(2)ge6,5x_(1)+x_(2)ge10 and x_(1),x_(2)ge0 , is

Check whether the following equations are quadratic or not . (i) x^(2) - 6x - 4 = 0 (ii) x^(3) - 6x^(2) + 2 x - 1 = 0 (iii) 7x = 2x^(2) (iv) x^(2) + (1)/(x^(2)) = 2 (v) (2x + 1 ) (3 x + 1 ) = 6 (x - 1) (x - 2) (vi) 3y^(2) = 192

Maximize z = 7x_(1) + 3x_(2) by graphical method Subjecto to x_(1) + 2x_(2) ge 3 x_(1) + x_(2) le 4 0 le x_(1) le (5)/(2) and 0 le x_(2) le (3)/(2)

Find the roots of the following quadratic equations (if they exist) by the method of comleting the square: (1) 2x^(2)+x-4=0 " "(2) 6x^(2)+18x+10=0 (3) x^(2)+5x+7=0" "(4)x^(2)+3sqrt(3)x-12=0