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Introduction to sum of roots and product of roots
For a quadratic equation a^2 + bx + c = 0 where a ≠ 0.
Sum of roots α + β = - b ÷ a
Product of roots α X β = c ÷ a
A quadratic equation can be written in the form x^2 - (sum of roots) x + (product of roots) = 0.
Please note that the following video shows the proof for the above statements. You need not remember this proof though it is interesting to know how the statements are derived. However, the above statements are important to remember.
Sum of roots α + β = - b ÷ a
Product of roots α X β = c ÷ a
A quadratic equation can be written in the form x^2 - (sum of roots) x + (product of roots) = 0.
Please note that the following video shows the proof for the above statements. You need not remember this proof though it is interesting to know how the statements are derived. However, the above statements are important to remember.
Solving questions on sum and product of roots
E.g.1: If α and β are the roots of the equation 2x^2 - 3x - 2 = 0, find α^2 + β^2, (α - β)^2 and α^3 + β^3 without solving the equation.
E.g. 2: If one root of the quadratic equation x^2 + px + q = 0 is twice the other root, find the relation between p and q.
E.g. 2: If one root of the quadratic equation x^2 + px + q = 0 is twice the other root, find the relation between p and q.