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Quadratic and Line Intersection
The quadratic y = x2 + 8 x + 13 and the line y = –6 x – 40 have points in common
at coordinates ( , )and ( , )

tickcross


Worked Solution:

Where the quadratic meets the line we have y = x2 + 8 x + 13 = –6 x – 40
=>x2 + 8 x + 13 = –6 x – 40
=>x2 + 14 x + 53 = 0
The discriminant for this quadratic is b2 – 4 ac = 142 – 4×1×53 = –16
This is negative, so there are no real roots and so no common points.

© MEI Produced by Dr Ron Knott, 20 July 2004, revised 12 May 2008
tom . button [AT] mei . org . uk 		Test reference: SimQuadLine.html?ref=20452