Question

Solve the following quadratic equations by any method. The solutions are:

f (x) = x 2 − 12x + 32
a.

(X - 4)(X - 8) this means that X = 4 and -8
b.

(X - 4)(X - 8) this means that X = -4 and -8
c.

(X - 4)(X - 8) this means that X = +4 and +8
d.

(X - 4)(X - 8) this means that X = -4 and +8

Answer 1

Option C .

Explanation:

We would like to solve the below quadratic equation ,

`\longrightarrow f(x) = x^2-12x +32`

Step 1 : Equate f(x) with 0 :-

`\longrightarrow f(x) = 0\\`

`\longrightarrow x^2-12x + 32=0`

Step 2 : Factorise the RHS :-

`\longrightarrow x^2-8x - 4x +32=0\\`

`\longrightarrow x(x-8)-4(x-8)=0\\`

`\longrightarrow (x-8)(x-4)=0\\`

Step 3 : Equate each factor with 0 :-

`\longrightarrow x - 8 = 0\\ \qquad x -4=0`

`\longrightarrow x = 8 \qquad x = 4`

`\longrightarrow \underline{\underline{\boldsymbol{ x = 8,4}}}`

Hence option C is correct .