as level discriminant question
hi, can anyone help me work out how to do this?
find the value of a for which
x^2 -4x +a
is always positive
find the value of a for which
x^2 -4x +a
is always positive
Original post by gingerxo
hi, can anyone help me work out how to do this?
find the value of a for which
x^2 -4x +a
is always positive
find the value of a for which
x^2 -4x +a
is always positive
Well for the curve to always be positive it must not touch or cross the x axis
Therefore it has no real roots
Posted from TSR Mobile
Complete the square and see if you can spot anything.
Original post by 42meaningoflife
Complete the square and see if you can spot anything.
completing the square gets (x-2)^2 -2 +a?? i'm acc so confused lol
As it's a discriminant question, you're looking at the b^2-4ac part of the quadratic formula. If the equation is always positive, b^2-4ac must be equal to 0.
Therefore, 4^2-4(1)(a)=0
Therefore 16-4a=0
Therefore 4a=16
Therefore a=4.
This should be the right answer if I've read you correctly (I'm sure I have!!)
Therefore, 4^2-4(1)(a)=0
Therefore 16-4a=0
Therefore 4a=16
Therefore a=4.
This should be the right answer if I've read you correctly (I'm sure I have!!)
Sorry, sorry - I did read you wrong you're right - it should be greater than 4!!
If you look at you're completing the square, you'll see that x=2 - this is actually the x coordinate of the minimum point. Therefore, b^2-4ac<0 as there are no real roots (you can tell because it doesn't cross the x axis).
Therefore, 4^2-4(1)(a)<0
Therefore 16<4a
Therefore a>4
As this is the case, does the question want a value for a or a set of values. If it wants a set of values, then this is you're answer. If it's wanting a specific value then I'm afraid I'm not too sure where to go from here.
If you look at you're completing the square, you'll see that x=2 - this is actually the x coordinate of the minimum point. Therefore, b^2-4ac<0 as there are no real roots (you can tell because it doesn't cross the x axis).
Therefore, 4^2-4(1)(a)<0
Therefore 16<4a
Therefore a>4
As this is the case, does the question want a value for a or a set of values. If it wants a set of values, then this is you're answer. If it's wanting a specific value then I'm afraid I'm not too sure where to go from here.
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