Question

solve the given quadratic equation 2x²-6x+3=0​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ 2x² - 6x + 3 = 0.

As we know that,

⇒ D = Discriminant Or b² - 4ac.

⇒ D = (-6)² - 4(2)(3).

⇒ D = 36 - 24.

⇒ D = 12.

As we know that,

⇒ α = -b + √D/2a.

⇒ β = -b - √D/2a.

⇒ α = -(-6) + √12/2(2).

⇒ α = 6 + √12/4.

⇒ α = 6 + 2√3/4.

⇒ α = 2(3 + √3)/4.

⇒ α = (3 + √3)/2.

⇒ β = -(-6) - √12/4.

⇒ β = 6 - √12/4.

⇒ β = 2(3 - √3)/4.

⇒ β = (3 - √3)/2.

                                                                                                                     

MORE INFORMATION.

Conjugate roots.

If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

x = 3+√3/2 or 3-√3/2

Step-by-step explanation:

2x²-6x+3=0

Now, We are going to solve the given quadratic equation using quadratic formula method.

2x²-6x+3=0

Here,

=> b = -6

=> a = 2

=> c = 3

Quadratic Formula:

x => -b+√D/2a or -b-√D/2a

D = Discriminant = b²-4ac

For the following equation, the discriminant is:

=> D = (-6)²-4×2×3

=> D = 36-24

=> D = 12

Hence, on applying the formula, we get:

x => -b+√D/2a or -b-√D/2a

x => 6+√12/4 or 6-√12/4

x => 2(3+√3)/4 or 2(3-√3)/4

x => 3+√3/2 or 3-√3/2

Hence, Solved!