# ×² + 4× + 3 =0, Can u help me find the value of the coefficients a, b and c?

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### Tanong

×² + 4× + 3 =0, Can u help me find the value of the coefficients a, b and c?

### Mga sagot sa #1 sa Tanong: ×² + 4× + 3 =0, Can u help me find the value of the coefficients a, b and c?

**Answer:**

You can solve any quadratic equation by completing the square—rewriting part of the equation as a perfect square trinomial. If you complete the square on the generic equation ax2 + bx + c = 0 and then solve for x, you find that . This equation is known as the Quadratic Formula.

This formula is very helpful for solving quadratic equations that are difficult or impossible to factor, and using it can be faster than completing the square. The Quadratic Formula can be used to solve any quadratic equation of the form ax2 + bx + c = 0.

Standard Form

The form ax2 + bx + c = 0 is called standard form of a quadratic equation. Before solving a quadratic equation using the Quadratic Formula, it's vital that you be sure the equation is in this form. If you don't, you might use the wrong values for a, b, or c, and then the formula will give incorrect solutions.

Example

Problem

Rewrite the equation 3x + 2x2 + 4 = 5 in standard form and identify a, b, and c.

3x + 2x2 + 4 = 5

3x + 2x2 + 4 – 5 = 5 – 5

First be sure that the right side of the equation is 0. In this case, all you need to do is subtract 5 from both sides.

3x + 2x2 – 1 = 0

2x2 + 3x – 1 = 0

Simplify, and write the terms with the exponent on the variable in descending order.

2x2

+

3x

–

1

=

0

↓

↓

↓

ax2

bx

c

a = 2, b = 3, c = −1

Now that the equation is in standard form, you can read the values of a, b, and c from the coefficients and constant. Note that since the constant 1 is subtracted, c must be negative.

Answer

2x2 + 3x – 1 = 0; a = 2, b = 3, c = −1

Example

Problem

Rewrite the equation 2(x + 3)2 – 5x = 6 in standard form and identify a, b, and c.

2(x + 3)2 – 5x = 6

2(x + 3)2 – 5x – 6 = 6 – 6

First be sure that the right side of the equation is 0.

2(x2 + 6x + 9) – 5x – 6 = 0

2x2 + 12x + 18 – 5x – 6 = 0

2x2 + 12x – 5x + 18 – 6 = 0

2x2 + 7x + 12 = 0

Expand the squared binomial, then simplify by combining like terms.

Be sure to write the terms with the exponent on the variable in descending order.

2x2

+

7x

+

12

=

0

↓

↓

↓

a

b

c

a = 2, b = 7, c = 12

Now that the equation is in standard form, you can read the values of a, b, and c from the coefficients and constant.

Answer

2x2 + 7x + 12 = 0; a = 2, b = 7, c = 12

**Step-by-step explanation:**

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