Question

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Answer 1

ANSWER

1. No solution

2. 4 and 6

3. 81

EXPLANATION

1. The given quadratic equation is

${x}^{2} + 1 = 0$

This implies that:

${x}^{2} = - 1$

There is no real number whose square is negative one.

This quadratic equation has no solution.

2. The given quadratic equation is

${x}^{2} - 10x + 24 = 0$

We split the middle term with -6,-4 because their product is 24 and their sum is -10

${x}^{2} - 6x - 4x+ 24 = 0$

We factor by grouping

${x}(x - 6)- 4(x - 6)= 0$

$(x - 6)(x - 4)= 0$

We have x=4 and x=6.

3. The given quadratic equation is

${x}^{2} - 18x = 7$

We the square of half the coefficient of x to both sides of the equation.

$( - \frac{18}{2} )^{2} = ( { - 9)}^{2} = 81$

The correct choice is C.