1.Standard form of Quadratic equation : ax² + bx + c = 0.........(1)
2.Roots of the equation (1) are x = {-b ± √(b² – 4ac)}/2a
3.If α and β be the roots of the equation (1) then,
sum of its roots = α + β = - b/a = - (coefficient of x)/(coefficient of x² );
and product of its roots = αβ = c/a = (Constant term /(Coefficient of x²).
4.The quadratic equation whose roots are α and β is,
x² - (α + β)x + αβ = 0
i.e. , x² - (sum of the roots) x + product of the roots = 0.
5.The expression (b² - 4ac) is called the discriminant of equation (1).
6.If a, b, c are real and rational then the roots of equation (1) are
(a) real and distinct when b² - 4ac > 0;
(b) real and equal when b² - 4ac = 0;
(c) imaginary when b² - 4ac < 0;
(d) rational when b²- 4ac is a perfect square
(e) irrational when b² - 4ac is not a perfect square.
7.If α + iβ be one root of equation (1) then its other root will be conjugate complex quantity α - iβ and conversely (a, b, c are real).
8.If α + √β be one root of equation (1) then its other root will be conjugate irrational quantity α - √β (a, b, c are rational).
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