Quadratic Equations Worksheet With Answer Key Page 7
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7Lecture – 27 (50 minutes)
a) Exercise of the problems related to quadratic equations.
b) Assignment
A. Exercise of the problems related to quadratic equations.
1. Determine the nature of the roots of the equations
2
2
i)x
– 4x + 3 = 0
ii) 2x
-6x +7 =0
2
iii) x
- 4x + 1
2
2
2. For what values of a will the equation x
- (3a -1)x +
2(a
- 1) = 0 have equal
roots?
2
3. If the roots of the quadratic equation 9x
-6x+k=0 are equal find the value of k.
2
4. Find the value of k so that the equation 2x
+kx -15 = 0 has one root 3.
5. Form a quadratic equation whose roots are the reciprocals of the roots of
2
2x
+ 5x + 4 = 0.
B. Assignment.
2
1. Find the value of k so that the equation 3x
+kx -2 = 0 has roots whose sum is 6.
2
2. If 2x
+ (4 - k)x - 17 = 0 has roots equal but opposite
in sign, find the value of k.
2
3. Find the value of k so that the equation 3x
+ 7x + 6 - k = 0 has one root equal to zero.
2
2
4. If the roots of ax
+ bx +c = 0 be in the ration 3:4, prove that 12b
= 49ac.
[Hints: take one root 3α and other 4α. Then using sum of roots = -b/a, find the value of α
and put that value in the relation of product of roots.]
2
2
5. If one root of the equation x
- px + q = 0 be twice the other, show that 2p
= 9q.
2
6. For what values of m, the equation x
-mx +m + 1 = 0 may have its roots in the ratio
2:3?
2
7. What are the roots of ax
+ bx + c = 0.
2
2
2
2
2
8. If the roots of (a
+ b
) x
- 2(ac + bd) x + (c
+ d
) = 0 are equal show that ad = bc.
9. Form the quadratic equation in which roots are 3, -2.
10. Find the quadratic equation whose roots are the reciprocals of the roots of
2
3x
– 5x –2 = 0
11. Form the quadratic equation whose roots will be
2
a) m times the roots of x
- px +q = 0.
2
b) greater by h than the roots of x
- px + q = 0.
2
c) the reciprocals of the roots of the equation ax
+ bx + c = 0.
2
-1
12. If α and β are the roots of ax
+ bx +c = 0, find the equation whose roots are αβ
and
-1
βα
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