Question

if b=a+c,then the roots of equation ax^2+bx+c

Answer 1

Here is your answer:

ax² + x(a+c) + c
ax² + ax + cx + c
ax(x+1) + c(x+1)
(x+1) (ax+c)

Answer 2

Answer:

The roots of the quadratic equation${ax^{2}+bx+c=0}$ are

$\boxed{x = - 1}$ OR $\boxed{x = \frac{-c}{a}}$

Step-by-step-explanation:

The general form of the quadratic equation is ax² + bx + c = 0.

Also, b = a + c ... [ Given ]

∴ ax² + bx + c = 0

∴ ax² + ( a + c )x + c = 0 ... [ By putting the given value of b. ]

∴ ax² + ax + cx + c = 0 .. [ By using ( a + b ) × c = ab + bc ]

∴ ax ( x + 1 ) + c ( x + 1 ) = 0

∴ ( x + 1 ) ( ax + c ) = 0

∴ ( x + 1 ) = 0 OR ( ax + c ) = 0

∴ x + 1 = 0 OR ax + c = 0

∴ x = - 1 OR ax = - c

∴ x = - 1 OR x = - c / a

Ans.: The roots of the quadratic equation ${ax^{2}+bx+c=0}$ are

$\boxed{x = - 1}$ OR $\boxed{x = \frac{-c}{a}}$

Additional Information:

1. Quadratic Equation :

An equation having a degree ‘2’ is called quadratic equation.

The general form of quadratic equation is

ax² + bx + c = 0

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

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Formula for finding roots of quadratic equation:

If the quadratic equation is

${ax^{2}+bx+c=0}$

Then,

$\boxed{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}}$