6. Show that the product of the roots of a quadratic equation ax
2
+ bx + c = 0 (a¹ 0) is
c
a
.
7. If the sum of the fraction and its reciprocal is 2 16
21
, find the fraction
What We Have Disuccused
1. Standard form of quadratic equation in variable x is ax
2
+ bx + c = 0, where a, b, c are
real numbers and a ¹ 0.
2. A real number a is said to be a root of the quadratic equation ax
2
+ bx + c = 0, if
aa
2
+ ba + c = 0. The zeroes of the quadratic polynomial ax
2
+ bx + c and the roots of
the quadratic equation ax
2
+ bx + c = 0 are the same.
3. If we can factorise ax
2
+ bx + c, a ¹ 0, into a product of two linear factors, then the roots
of the quadratic equation ax
2
+ bx + c = 0 can be found by equating each factor to zero.
4. A quadratic equation can also be solved by the method of completing the square.
5. Quadratic formula: The roots of a quadratic equation ax
2
+ bx + c = 0 (a ¹ 0) are given
by
2
4
,
2
-± - b b ac
a
provided b
2
– 4ac > 0.
6. A quadratic equation ax
2
+ bx + c = 0 (a ¹ 0) has
(i) two distinct real roots, if b
2
– 4ac > 0,
(ii) two equal roots (i.e., coincident roots), if b
2
– 4ac = 0, and
(iii) no real roots, if b
2
– 4ac < 0.