2.4 Discriminant of a quadratic function

AQA Edexcel OCR A OCR B (MEI)
For the quadratic function \(f(x)=ax^2+bx+c\), the expression \(b^2-4ac\) is known as the discriminant. The value of the discriminant tells you how many roots \(f(x)\) has.
  • If \(b^2-4ac>0\), \(f(x)\) has two real roots, and \(y=f(x)\) will cross the x-axis twice.
  • If \(b^2-4ac=0\), \(f(x)\) has one repeated root, and \(y=f(x)\) will touch the x-axis once.
  • If \(b^2-4ac<0\), \(f(x)\) has no real roots, and \(y=f(x)\) will not cross the x-axis.

If the question refers to two/one/no solutions, or graphs intersecting/touching/not intersecting each other, then it is likely that you will need to use the discriminant to do the question.
Important
For the quadratic function \(f(x)=ax^2+bx+c\), the discriminant (\(b^2-4ac\)) tells you how many roots the function has.

  • If \(b^2-4ac>0\), \(f(x)\) has two real roots.
  • If \(b^2-4ac=0\), \(f(x)\) has one repeated root.
  • If \(b^2-4ac<0\), \(f(x)\) has no real roots.
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