Alex robert
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  • roots of Quadratic Equation

 

    • For a quadratic equation ax2 + bx + c where a ≠ 0, the roots will be given by the equation as b±b2−4ac2a
    • Δ = b2 − 4ac is called the discrimination
    • For real and distinct roots, Δ > 0
    • For real and coincident roots, Δ = 0
    • For non-real roots, Δ < 0
    • If α and β are the two roots of the equation ax2 + bx + c then, α + β = (-b / a) and α × β = (c / a).
    • If the roots of a quadratic equation are α and β, the equation will be (x − α)(x − β) = 0
    • Factorials

§   

        • n! = (1).(2).(3)…..(n − 1).n
        • n! = n(n − 1)! = n(n − 1)(n − 2)! = ….
        • 0! = 1
        • (a+b)n=an+nan−1b+n(n−1)2!an−2b2+n(n−1)(n−2)3!an−3b3+….+bn,where,n>1

 

Algebra Formulas -2

Solved Examples

Question 1: Find out the value of 52 – 32
Solution:
Using the formula a2 – b2 = (a – b)(a + b)
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2 × 8
= 16
Question 2: 43 × 42 = ?
Solution:
Using the exponential formula (am)(an) = am+n
where a = 4
43 × 42
= 43+2
= 45
= 1024

 

 
Alex robert
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