Question

write the root of quadratic equation (x+6) (x-3) =0​

Answer 1

Step-by-step explanation:

x^2-3x+6x-18

x^2+3x-18

x^2+6x-3x-18

x(x+6)-3(x+6)

(x-3)(x+6)

x=3 or -6

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Answer 2

Answer:

The roots of the quadratic equation $(x+6)(x-3) = 0$ are 3 and -6.

Step-by-step explanation:

What is the root of a quadratic equation?

The root of a quadratic equation is defined as the values of the variables satisfying the quadratic equation. In simple words, a root is the solution of a quadratic equation. That is, x = a is a root of the quadratic equation $f(x) = ax^{2} +bx+c$ if f(a) = 0. There are different methods for finding the roots of a quadratic equation. They are:

• Factoring
• Quadratic formula
• Square completion
• Graphing

Given:

Quadratic equation $(x+6)(x-3)=0$

i) By Factoring method:

$(x+6)(x-3)=0$

⇒ $x+6=0,\ x-3 =0$

⇒ $x=-6, \ x=3$

ii) By quadratic formula:

Given quadratic equation can be written as,

$(x+6)(x-3)=0$

⇒ $x^{2} -3x+6x-18 =0$

⇒ $x^{2} + 3x-18=0$

⇒ $x= \frac{-b \pm \sqrt{b^{2} - 4ac } }{2a}$               $[a=1, \ b=3, \ c=-18]$

⇒ $x= \frac{-3 \pm \sqrt{3^{2} - (4 \times -18) } }{2}$

⇒ $x= \frac{-3 \pm \sqrt{9+72} }{2}$

⇒ $x= \frac{-3 \pm \sqrt{81} }{2}$

⇒ $x=\frac{-3 \pm 9}{2}$

⇒ $x = \frac{-3+9}{2}, \ \frac{-3-9}{2}$

⇒ $x = 3, \ -6$

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