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    hi guys

    Name:  roots.png
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    please can someone help me with understanding the question? the use of the quadratic formula is fine, and maybe i'm being a bit slow here, but i don't understand the second line in the answer - "the difference in roots is ... " where do we get the 1/2 from, and although I know the difference is supposed to be 2, why exactly do we make the equation equal to 2?

    thank you in advance

    The quadratic formula gives you two roots. The difference between the two roots is one root subtracted from the other one. If you actually do that subtraction, should get to the second line in the answer.

    The question tells you that the difference between the roots is 2, so you are entitled to make your expression obtained above equal to 2.

    From there, it's just a matter of rearranging the equation to make c the subject.

    the point on the x axis exactly half way between the roots is -b/2a.... the distance from this point to the right hand root is {√( b2 - 4ac)}/2a

    so you need to double that distance to find the separation of the two roots.
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