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This method is convenient but is not applicable to every equation. Solving these equations for x gives: x=-4 or x=1. Thus we have either (x+4) = 0 or (x-1) = 0 or both are = 0.
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For any two quantities a and b, if a×b = 0, we must have either a = 0, b = 0 or a = b = 0. Thus, we can factorise the terms as: (x+4)(x-1) = 0. Hence, we write x 2 + 3x – 4 = 0 as x 2 + 4x – x – 4 = 0. Consider (+4) and (-1) as the factors, whose multiplication is -4 and sum is 3. We do it such that the product of the new coefficients equals the product of a and c. Next, the middle term is split into two terms. Solution: This method is also known as splitting the middle term method. Examples of FactorizationĮxample 1: Solve the equation: x 2 + 3x – 4 = 0 Let’s see an example and we will get to know more about it. Hence, from these equations, we get the value of x. These factors, if done correctly will give two linear equations in x. Certain quadratic equations can be factorised. So those are the points where, those are the x-values where the function intersects the x-axis.The first and simplest method of solving quadratic equations is the factorization method. So, also the point negative one comma zero is on this graph. And also, if x is equal to negative one, negative one minus two, negative three. So, the point five comma zero is going to be on this graph. If x is equal to five,įive minus two is three, squared is nine, minus nine is zero. Well, you add two to both sides of this, you get x is equal to five, or x is equal to, if weĪdd two to both sides of this equation, you'll get Is equal to positive three or x minus two is equal to negative three. And just like we saw before, that means that x minus two is equal to the positive or negative square root of nine. Sides and so we could get x minus two squared is equal to nine. So we could rewrite this as x, x minus two squared minus nine equals zero. This thing right over here "equal zero?" So, let me just write that down. X-values where the graph of y equals f of x intersects the x-axis, this is equivalent to saying, "For what x-values doesį of x equal zero?" So we could just say, "For what x-values does
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And that means that ourįunction is equal to zero. Notice our y-coordinateĪt either of those points are going to be equal to zero. Well, in order to intersect the x-axis, y must be equal to zero. The x-values where you intersect, where you intersect the x-axis. Let's say that the y isĮqual to some other function, not necessarily this f of x. If I have the graph of some function that looks something like that. Talking about some graph, so I'm not necessarily gonnaĭraw that y equals f of x. And then we're asked at what x-values does the graph of y equalsį of x intersect the x-axis. So, we are told that f of x isĮqual to x minus two squared minus nine. That's presented to us in a slightly different way. So, these are the two possible x-values that satisfy the equation. And when x is equal to negative five, negative five plus three is negative two, squared is positive four, minusįour is also equal to zero. You substitute it back in if you substitute x equals negative one, then x plus three is equal to two, two-squared is four, minus four is zero. Substitute it back in, and then you can see when So, those are the two possible solutions and you can verify that. Negative two minus three is negative five. Or, over here we could subtract three from both sides to solve for x. Sides to solve for x and we're left with x isĮqual to negative one. So, if x plus three isĮqual to two, we could just subtract three from both If x plus three was negative two, negative two-squared is equal to four. Notice, if x plus three was positive two, two-squared is equal to four. And so we could write that x plus three couldīe equal to positive two or x plus three could beĮqual to negative two. Positive square root of four or the negative square root of four.
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Something right over here, is going to be equal to the If something-squared is equal to four, that means that the something, that means that this Three is going to be equal to the plus or minus So, one way of thinking about it is, I'm saying that x plus Way of thinking about it, if I have something-squared equaling four, I could say that that something needs to either be positive or negative two. And so now, I could take the square root of both sides and, or, another So, x plus three squared is equal to four. So, adding four to both sides will get rid of thisįour, subtracting four, this negative four on the left-hand side. This is I'm gonna isolate the x plus three squared on one side and the best way to do that The video and see if you can solve for x here.