(Summary ) (1 – 4 ) The Relation Between the Roots of the Second Degree Equation and the Coefficients of its Terms.

 

 

1sec ≫ First term  ≫ Algebra ≫ Unit 1 ≫(1 – 4 ) The Relation Between the Roots of the Second Degree Equation and the Coefficients of its Terms.

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(summary)

The relationship between the two roots of the equation \(ax^2 + bx + c = 0\) and its coefficients:

• Sum of the two roots: \( -\frac{b}{a} \)
• Product of the two roots: \( \frac{c}{a} \)

In the quadratic equation: \( ax^2 + bx + c = 0 \)

If \(a = 1\), then \(L + M = -b\) and \(LM = c\)

i.e., The sum of the two roots equals the negative coefficient of \(x\),
the product of the two roots equals the absolute term.

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If \(b = 0\), then \(L + M = 0\), i.e., \(L = -M\)

i.e., One of the two roots of the equation is the additive inverse of the other.

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If \(a = c\), then \(LM = 1\); i.e., \(L=\frac{1}{M}\)

i.e., One of the two roots of the equation is the multiplicative inverse of
the other.

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Forming Quadratic Equation Whose Two Roots are Known

If the roots of the quadratic equation are known, the quadratic equation can be formed as follows:

$$x^2 - (\text{sum of the two roots})x + \text{the product of the two roots} = 0$$