*The factoring method is an easy way of finding the roots.*

The quadratic formula to find the roots, x = [-b ± √(b 2x-6 = 0 Here, a = 1, b=2 and c= -6. → x = [-2 ± √(4*7)] / 2 → x = [-2 ± 2√7] / 2 → x = 2[ -1 ± √7] / 2 → x = -1 ± √7 Hence, √7-1 and -√7-1 are the roots of this equation. Solve for x: x 10x-24 = 0 What are the two numbers which when added give 10 and when multiplied give -24?

Substituting these values in the formula, x = [-2 ± √(4 – (4*1*-6))] / 2*1 → x = [-2 ± √(4 24)] / 2 → x = [-2 ± √28] / 2 When we get a non-perfect square in a square root, we usually try to express it as a product of two numbers in which one is a perfect square.

- [Instructor] What are all the solutions to the equation above?

And we have x plus three times x minus five is equal to five. In order to kind of make the factoring useful, you have to be able to say, hey, the product of these two things is equal to zero, because if the product of two things is equal to zero, then you know that either one or the both of them need to be equal to zero.

The questions progress well so that students can get a good conceptual understanding of every major topic.

A disciplined practice through this book prepares the students for both examinations fully. So we can just resort to the quadratic formula here. So this would be the same thing as the square root of four times the square root of 21, which of course is two times the square root of 21, all of that over two. So the roots are going to be x is equal to negative b. So negative of negative two is gonna be positive two, plus or minus the square root of b squared, which is four, minus four times a, which is one, times negative 20. And since that's a negative 20 but I'm subtracting it, I could put a plus there. But let's see if we can get to the right solution here. This is going to, x is going to be equal to two plus or minus.When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster ... and a Quadratic Equation tells you its position at all times! There are many ways to solve it, here we will factor it using the "Find two numbers that multiply to give a×c, and add to give b" method in Factoring Quadratics: a×c = A very profitable venture.Your company is going to make frames as part of a new product they are launching.You wanna be very careful here because you're probably have some experience with algebra that, hey, once I factored it out, maybe I could say, okay, maybe this needs to be equal to five, or this needs to be equal to five. So we've actually have to do a lot of algebraic manipulation here to get it into that form, but let's see if we can do it. So the first thing I would do is just multiply out x plus three times x minus five. Well it's going to be x times x, which is x squared, plus x times negative five. Quadratic equations are also needed when studying lenses and curved mirrors.And many questions involving time, distance and speed need quadratic equations.I highly recommend the following textbook for both GCSE(9-1) and IGCSE(9-1).The book covers every single topic in depth and offers plenty of questions to practise.

## Comments Problem Solving Quadratic Equations

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