X-Matric Formula Algebra

ALGEBRA

Remainder theorem.

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) .

Factor theorem

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).

Quadratic Equation

1. General quadratic Equation is

ax² + bx + c = 0, where a, b, c are real and a ≠ 0.

2. Roots
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

Discriminant Δ = b2 - 4ac	Nature of Roots
Δ > 0 but not a perfect square Δ > 0 and a perfect square Δ = 0 Δ <>	Real, unequal and irrational Real, unequal and rational Real and equal Unreal