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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

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VirαtKσhli

Answer:

Option C .

Step-by-step explanation:

We would like to solve the below quadratic equation ,

[tex]\longrightarrow f(x) = x^2-12x +32 [/tex]

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

[tex]\longrightarrow f(x) = 0\\[/tex]

[tex]\longrightarrow x^2-12x + 32=0[/tex]

Step 2 : Factorise the RHS :-

[tex]\longrightarrow x^2-8x - 4x +32=0\\[/tex]

[tex]\longrightarrow x(x-8)-4(x-8)=0\\[/tex]

[tex]\longrightarrow (x-8)(x-4)=0\\[/tex]

Step 3 : Equate each factor with 0 :-

[tex]\longrightarrow x - 8 = 0\\ \qquad x -4=0 [/tex]

[tex]\longrightarrow x = 8 \qquad x = 4 [/tex]

[tex]\longrightarrow \underline{\underline{\boldsymbol{ x = 8,4}}}[/tex]

Hence option C is correct .

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