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| Summary |
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- i) An expression of the form a0xn
+ a1xn-1+....+ an
= 0, where n is a positive integer and a0, a1,...,an belong to
some number system F, is called a polynomial in the variable x over F.
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- ii) The degree of polynomial is defined as the highest index of the variable x occurring in the polynomial.
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| i) An identity is a statement of equality between two expressions
which is true for all values of the variable involved. |
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| ii) An equation is a statement of equality between two expressions
which is not true for all values of the variable involved. |
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- If f(x)=0 is a polynomial equation and f(a)=0, then 'a' is a root of the polynomial equation.
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If ax2 + bx + c = 0, a = 0,
then  where a, b, c be any
complex numbers. |
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- A quadratic equation has exactly two roots.
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- For the quadratic equations, we have
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i) b2 - 4ac > 0  Roots are real and distinct |
ii) b2 - 4ac = 0  Roots are real and equal |
iii) b2 - 4ac < 0  Roots are imaginary and distinct |
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- If the roots of ax2 + bx + c = 0, a(¹
0),b, c Î R, are a
and b, then
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- An expression in a, b is called a symmetric function of
a, b if the expression is not affected by interchanging
a and
b.
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- The quadratic equation with roots a
and b is given by x2- Sx + P = 0 where S =
a + b and P =
ab.
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