1.

3. Determine the nature of roots of the following quadratic equations.x²-4x+4=0​

Answer»

Given:

  • Equation → x² - 4x + 4

To find:

Nature of roots = ?

FORMULA USED:

\rm{For \: finding\:the\:nature\:of\:roots,}\\\\\bf{D = b^{2} - 4ac}\\\\\tt{where,}\\\\\star \quad \sf{D=Discriminant}\\\star \quad \sf{a = <klux>1</klux>}\\\star \quad \sf{b = -4}\\\star \quad \sf{c=4}

D = b² - 4ac

⇒ D = (-4)² - 4(1)(4)

⇒ D = 16 - 16

∴ D = 0

Since D = 0, the given quadratic equation has 1 real and equal root.

Additional Information:

  1. If D > 0, the equation will have 2 real and distinct roots.
  2. If D < 0 , the equation will have 2 non real or imaginary roots.


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