If a polynomial P(x) of degree ≥ 1 over the set of real numbers
R is divided by x-a where a є R then the remainder is P(a) .
If P(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number then
1. (x-a) is a factor of P(x) if P(a) = 0
2. P(a) = 0 if (x-a) is a factor of P (x).
1. General quadratic Equation is
ax2 + bx + c = 0, where a, b, c are real and a ≠ 0.
x = (-b +√ b2-4ac) /2a
3. If a and b are the roots then the required equation is
x2 - (a+b) x + (ab)=0
4. Sum of the Roots (a+b) = –b / a
5. Product of the Roots (ab) = c / a
Nature of Roots
Δ > 0 but not a perfect square
Δ > 0 and a perfect
Real, unequal and irrational
Real, unequal and rational
Real and equal