Question

3x² - 12x +9=0 using quadratic formula

Answer 1

Answer:

The quadratic equation 3x² - 12x + 9 = 0 has two real roots when solved:

x₁ = 1 and x₂ = 3

Step-by-step explanation:

✍ An equation of type ax² + bx + c = 0, can be solved, for example, using the quadratic formula:

$\boldsymbol{x=\dfrac{-b\pm\sqrt{b^{2}-4ac } }{2a} }$

either

$\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} }$

where

$\bf{\Delta=b^{2}-4ac }$

Identify the coefficients

a = 3, b = -12 and c = 9

Calculate the discriminant value

Δ = b² - 4ac

Δ = (-12)² - 4.3.9 = 144 - 12.9

Δ = 144 - 108 = 36

Enter the values of a, b and the discriminant value in the quadratic formula

$\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta } }{2a} }$

$\boldsymbol{x=\dfrac{-(-12\pm\sqrt{36} }{2\cdot3 } }$

$\boldsymbol{x=\dfrac{(12\pm\sqrt{36} }{6 } \ ==== > \ (Solution \ general) }$

As we can see above, the discriminant (Δ) of this equation is positive (Δ> 0) which means that there are two real roots (two solutions), x₁ and x₂.

$\boldsymbol{x_{1}=\dfrac{-12-\sqrt{36} }{6}=\dfrac{12-6}{6}=\dfrac{6}{6}=1 \ === > (First \ solution) }$

To find x₁, just choose the positive sign before the square root. Later,

$\boldsymbol{x_{1}=\dfrac{12+\sqrt{36} }{6}=\dfrac{12+6}{6}=\dfrac{18}{6}=3 \ === > (Second \ solution) }$