Please help! I tried this problem but I couldn't get it quite right... Create a quadratic equation that cannot be solved by factoring, but can be solved by using the quadratic formula. Explain how you know it cannot be solved by factoring.
When a quadratic equation can't be factored, that just means that where it crosses the x-axis, it crosses at places that aren't rational numbers such as sqrt(20), 1.43867392957, etc. To create one of these equations you must make the discriminant not be equal to a perfect square. The discriminant is the part of the quadratic formula that is under the square root sign, it is written like sqrt(b^2 - 4ac) so to make it not factorable, make sure that b^2 - 4ac is not a perfect square (1, 4, 9, 16, 25...). Also make sure it is positive and not zero because if it is negative then it has no solutions anyways and if it is 0 then it is factorable.
THANK YOU SO MUCH!
Can you give me an example of numbers you would use? i tried x^2-4.25x+3.86=0 at first but i don't think that's right
That's right, because (-4.25)^2 is some number then subtract by 4 * 3.86 * 1 and you get 2 point something, and that is not a perfect square so you are good there
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