Question

Can someone explain the process of solving the quadratic equation below (including how to factorise the product) :-

7n^2 + 2407n - 61800 = 0

P.s. - I already know the answer. I want to know how to get -168n and 2575n as the factors.

Thanks

Answer 1

Explanation:

You get -168n and 2575n as the factors by using the sum-product pattern, to do this, you have to look at the terms and find the coefficients.

term 1 - 7n^2 and the coefficient is 7

term 2 - 2407n and the coefficient is 2407

term 3 - -61800 this is the constant, therefore there is no coefficient.

Then to solve the sum-product pattern, you have to multiply the first term by the constant. 7 · -61800

Then, you have to find factors of -432600 that also has a sum of the second term, 2407.

Anyway, the only two numbers that can make the number -432600 and has a sum of 2407 is -168 and 2575, which you then put into your equation as factors and solve.

The answer to the equation as a whole should be n = 24 and n = -2575/7