EXPLANATION.

Factorization.

⇒ x² - 12x + 27 = 0.

Factorize the equation into middle term splits, we get.

⇒ x² - 9x - 3x + 27 = 0.

⇒ x(x - 9) - 3(x - 9) = 0.

⇒ (x - 3)(x - 9) = 0.

⇒ x = 3  and  x = 9.

MORE INFORMATION.

Nature of the roots of quadratic expression.

(1) Roots are real and unequal, if b² - 4ac > 0.

(2) Roots are rational and different, if b² - 4ac is a perfect square.

(3) Roots are real and equal, if b² - 4ac = 0.

(4) If D < 0 Roots are imaginary and unequal Or complex conjugate.

Verified answer

Step-by-step explanation:

x2-12x+27=0

x2 -(9+3)x +27 [•split 12 in 9 and 3]

x2 -9x-3x +27 =0

x(x-9) -3(x-9)=0

(x-9) (x-3) =0

x-9=0, x-3=0

[x=9] , [x=3] answer

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