Question

How do you factor and solve $2x\left( x+3 \right)=0$ ?

Answer 1

Hint: The equation given in the question is already in factor form; we do not need to factor it. And another thing is that if a product of 2 numbers x and y is 0 then x can be 0 or y can be 0. We can use this to find the value of x in the equation $2x\left( x+3 \right)=0$ .

Complete step by step answer:
The equation given in the question is $2x\left( x+3 \right)=0$
We can see that the above equation is already in factor form, so we do not need to factor it.
We can see that product of 2x and x + 3 is equal to 0 , and we know that if product of 2 number a and b is 0 then the value of a can be 0 or b can be 0
So 2x = 0 or x + 3 = 0
So x can be 0 or -3 , the roots of the equation $2x\left( x+3 \right)=0$ are 0 and -3.

Note: We can find the roots of the equation by applying the quadratic equation formula $\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ . Where a is the coefficient of ${{x}^{2}}$ , b is the coefficient of x and c is the constant term of a quadratic equation. So if we expand the equation $2x\left( x+3 \right)$ it will be $2{{x}^{2}}+6x$ , so the value of a is 2 , value of b is 6 and the value of c is 0. So applying the formula $\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ the roots of the equation are $\dfrac{-6\pm \sqrt{{{6}^{2}}-4\times 2\times 0}}{2\times 2}$ so further solving we get
$\dfrac{-6\pm 6}{2\times 2}$ which is -3 and 0.