5. Quadratic Equation
£ It is the second degree equation, also said polynomial of
degree two.
£ The quadratic equation is derived from Latin language.
£ In Latin “Quadratus” means “Square”
6.
7. “The root of a number x is another number, its mean when a
number is multiplied to itself it gives number of times, equal x”.
Example:
The second root of 25 is 5, because 5 x5 = 25.
‡ The second root is called square root
‡ The third root is called cube root
8.
9. We know that and are the roots of the quadratic equation
where a, b are the co-efficient of and respectively, where
C is the constant term.
10. Relationship between roots and
quadratic equation
Let we consider and
then we find the sum and product of the roots.
We add both quadratic formulas alpha and beta
= +
Derivation
Relationship between roots and
quadratic equation
Sum of
roots
13. If we denote the sum and product of roots by
S and P respectively, then
14. œ The sum of the roots of the quadratic equation is
equal to the negation of the co-efficient of the
second term, dividing by the leading co-efficient.
œ The product of the roots of the quadratic equation is
equal to the constant term( the third term), divided by the
leading co-efficient.
16. Question No: 1
Find the relation between roots and co-efficient of a quadratic equation
without solving the equation
find sum and product
Solution:
Let be the roots of the given question.
Then,
17. Question No, 2
Find the relation when roots are connected by given relation.
Find relation between co-efficient of a, b and c of quadratic equation.
If alpha and beta are the roots of the equation
Find the values of the following;
(i)
(iv)
18. The given equation is
according to the problem alpha and Beta are the roots of the
equation
Therefore;
(i)
