Question

check weather the following are quadratic equation: x²-2x =(-2) (3-x) please make sure to tell me the full equation ​

Answer 1

EXPLANATION.

Equation : x² - 2x = (-2)(3 - x).

As we know that,

We can write equation as,

⇒ x² - 2x = - 2(3 - x).

⇒ x² - 2x = - 6 + 2x.

⇒ x² - 2x + 6 - 2x = 0.

⇒ x² - 4x + 6 = 0.

We know that,

Quadratic equation in the form of : ax² + bx + c where (a ≠ 0).

Hence the equation is quadratic equation.

                                                                                                                 

MORE INFORMATION.

Conjugate roots.

D = Discriminant Or b² - 4ac.

(1) If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

Answer:

Given :-

➳ x² - 2x = (- 2)(3 - x)

To Find :-

➳ Whether the following is a quadratic equation ?

Solution :-

Given Equation :

$\mapsto \bf x^2 - 2x =\: (- 2)(3 - x)$

By solving this equation we get,

$\implies \sf x^2 - 2x =\: (- 2)(3 - x)$

$\implies \sf x^2 - 2x =\: (- 2) \times (3 - x)$

$\implies \sf x^2 - 2x =\: - 6 + 2x$

$\implies \sf x^2 - 2x + 6 - 2x =\: 0$

$\implies \sf x^2 - 2x - 2x + 6 =\: 0$

$\implies \sf x^2 - 4x + 6 =\: 0$

$\implies \sf\bold{\red{x^2 - 4x + 6 =\: 0}}$

So, first let's us know what is quadratic equation :-

$\bigstar \: \: \sf\boxed{\bold{\pink{Quadratic\: Equation\: :-}}}\: \: \: \bigstar$

$\bullet$ A quadratic equation is a equation that can be written in a standard form :-

$\dashrightarrow \sf\bold{\purple{ax^2 + bx + c =\: 0}}$

where, a, b and c are real numbers and a ≠ 0.

So, let's compare that above equation with this standard form of quadratic equation :

$\leadsto \sf\bold{\green{x^2 - 4x + 6 =\: 0}}$

By comparing with ax² + bx + c = 0 we get,

◆ a = 1

◆ b = - 4

◆ c = 6

So, we can understand that the above equation is a quadratic equation.

$\therefore$ The given equation is a quadratic equation.

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EXTRA INFORMATION :-

$\clubsuit$ Quadratic Formula :

$\longrightarrow \sf\boxed{\bold{\pink{x =\: \dfrac{- b ± \sqrt{(b^2 - 4ac)}}{2a}}}}$

$\clubsuit$ Discriminant Formula :

$\longrightarrow \sf\boxed{\bold{\pink{Discriminant\: (D) =\: b^2 - 4ac}}}$

[Note :- The discriminant is a small part of the quadratic formula. ]