Question

1) Study the equation m² - 5m + 3 = 0 and write the answers of the following
questions.
a) Is this a quadratic equation? Why?
b) Can you solve this equation by factorization? Give reason.
c) If 3 is added to left side of the given equation then can you solve the new
equation by factorization. Give reason.​

Answer 1

Answer.

a) Yes, it is.

b) No, we can't.

c) Yes, we can.

Answer Keys.

• Quadratic Equation

An equation having the highest degree of 2.

• Factorization

Showing an expression as products.

Solution.

a) This equation has the highest degree of 2, because of $m^2$.

b) We cannot solve it through factorization, because this will involve square roots[1].

c) The new equation is $m^2-5m+6=0$. The two factors are $m-2,m-3$. For the product to be zero, each factor needs to be zero. Solutions are $m=2$ or $m=3$.

More information.

[1] We can solve $m^2-5m+3=0$ using complete the square method or quadratic formula. The solutions are $m=\dfrac{5\pm\sqrt{13}}{2}$.

Methods of Solving Quadratic Equation

• Factorization

For the expression to be zero, each factor needs to be zero. However, this may not work for some equations.

• Complete the Square Method

This involves the concept of the square root. This method is not used because it uses a lot of time.

• Quadratic Formula

This is a more generalized method of complete the square method. This works where factorization doesn't work.