Hello , I have been trying to solve this question for a long time but I can’t figure out the solution , could you please guide me .
Thanks and Regards
How have you been approaching it?
Hi, if you solve the given solution:
x^2 + 8x -16 <=0
this is a U-shaped parabola with some part of it under the x-axis. So we need to find out the sum of x-coordinates where the parabola hits the x-axis, which are the solutions for x^2 + 8x -16=0, and we know that the sum of roots of a quadratic equation ax^2+bx+c=0 is -b/a, from this we can get -8/1 as the sum max and min values possible for x satisfying x^2 + 8x -16 <=0 conditions.
this would be my approach. I hope it is helpful.
Hey ,
Thank you for your approach , I did it like this but the major issue I faced is how do we know if the sum of the roots is actually the sum of the maximum and minimum value of x.
as it was mentioned in the question,
x^2 + 8x -16 has to be less than or equal to zero, so we don’t need the part of it above the X-axis, if we consider only the lower part we can deduce that X’s maximum value is where the parabola hits X-axis on right, and the minimum is at the left intersection point. Hence the sum of max of x and min of x would be the sum of roots of the quadratic equation. (if we can imagine an upward U-shaped parabola with some part of it below the X-axis, we can see that it hits X-axis at the max and min values of X.)
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It is C. Just trying solving this as if you are solving regular quadratic equation
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Thanks !