ANSWER1. No solution2. 4 and 63. 81EXPLANATION1. The given quadratic equation is [tex] {x}^{2} + 1 = 0[/tex]This implies that:[tex] {x}^{2} = - 1[/tex]There is no real number whose square is negative one.This quadratic equation has no solution.2. The given quadratic equation is [tex] {x}^{2} - 10x + 24 = 0[/tex]We split the middle term with -6,-4 because their product is 24 and their sum is -10 [tex]{x}^{2} - 6x - 4x+ 24 = 0[/tex]We factor by grouping[tex]{x}(x - 6)- 4(x - 6)= 0[/tex][tex](x - 6)(x - 4)= 0[/tex]We have x=4 and x=6.3. The given quadratic equation is[tex] {x}^{2} - 18x = 7[/tex]We the square of half the coefficient of x to both sides of the equation.[tex]( - \frac{18}{2} )^{2} = ( { - 9)}^{2} = 81[/tex]The correct choice is C.