Question

solve for x : 3x^2 +2x =1 ​

Answer 1

Given :-

• A quadratic equation _ 3x² + 2x = 1

To Find :-

• Value of x

Solution :-

Given that,

3x² + 2x = 1

Steps to solve :-

Here, we can see that the coefficient of x² is 3.

For solving this equation, we need to multiply the constant c with 3 ( the coefficient of x²).

That's why, the product of numbers should be equal to

⟼ -3 ( 3 × -1)

Now, we can easily solve this problem expressing 2x as sum of +3x and -x.

3x² + 2x = 1

⟼ 3x² + 2x - 1 = 0

⟼ 3x ( x + 1) -1 ( x + 1) = 0

⟼ ( x + 1) ( 3x - 1) = 0

Hence,

( 3x - 1) = 0

⟼ 3 x = 1

⟼ x = ⅓

OR,

x + 1 = 0

⟼ x = -1

Verification :-

✞ 3x² + 2x = 1

⟼ 3 ( ⅓ )² + 2 ( ⅓) = 1

⟼ ⅓ + ⅔ = 1

⟼ 1 = 1

R.H.S = L.H.S

✞ 3x² + 2x = 1

⟼ 3 ( -1)² + 2 ( -1) = 1

⟼ 1 = 1

R.H.S = L.H.S

Hence, value of x = -1 , ⅓

$★{\underline{\underline{\large{\bold{More\:Information:-}}}}}$

✰ A standard quadratic equation can be expressed as

ax² + bx + c = 0

Where,

a = Coefficient of x²

b = Coefficient of x

c = Constant

and a ≥ 1

For example :-

x² + 5x + 6 = 0

Where,

1 and 5 are the coefficients of x² and x respectively. Here, 6 is the constant.

Answer 2

EXPLANATION.

Solve for x.

3x² + 2x = 1.

As we know that,

We can write equation as,

⇒ 3x² + 2x - 1 = 0.

Factorizes the equation into middle term splits, we get.

⇒ 3x² + 3x - x - 1 = 0.

⇒ 3x(x + 1) - 1(x + 1) = 0.

⇒ (3x - 1)(x + 1) = 0.

⇒ x = 1/3  and  x = - 1.

                                                                                                                   

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.