Quadratic Equations Worksheet With Answer Key Page 5
ADVERTISEMENT
1
2
3
4
5
6
7Example1:
Form a quadratic equation whose roots are 2 and 3.
Solution:
sum of roots = 2 + 3 = 5
product of roots = 2.3 = 6
so
required quadratic equation is
2
x
-(sum of roots)x + product of roots = 0
2
or x
- 5x + 6 = 0.
Example 2:
2
Form a quadratic equation whose roots are twice the roots of 3x
+ 5x + 1 = 0.
Solution:
2
comparing the given equation with ax
+ bx + c = 0, we get a = 3, b = 5 and c = 1.
suppose α and β are the roots of the given equation. Then
b
−
sum of roots(α + β) =
a
= -5/ 3.
c
product of roots( α . β )
=
a
= -1/3
According to the question, the roots of the new equation(i.e. required equation)
are 2 α and 2 β .
For this
sum of roots = 2 α + 2 β
= 2( α + β )
= 2. (-5/3)
= -10/3
product of roots = 2 α .2 β
= 4. αβ
= 4. (-1/3)
= -4/3.
Hence the required equation is
2
x
– (sum of roots)x + product of roots = 0.
2
or
x
– (-10/3)x + (-4/3) = 0
2
or
3x
+ 10x – 4 = 0.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education