Chapter 1 Quadratic Equations In One Unknown Worksheet With Answers Page 14
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34Number and Algebra
Number and Algebra
− 5x + 3 = 0
− 4x + 1 = 0
2
2
5.
12x
6.
4x
Solution
Solution
∆ = (−5)
− 4(12)(3)
∆ = (−4)
− 4(4)(1)
2
2
= 0
= −119
Q ∆ < 0
Q ∆ = 0
∴ The equation has a double real root.
∴ The equation has no real roots.
For each of the following quadratic equations, find the value or the range of possible values of m
with the given nature of roots. (7 – 12)
+ 8x + 2m = 0 has two distinct real roots.
2
7.
x
Solution
+ 8x + 2m = 0 has two distinct real roots.
Q
2
The equation x
∴
∆ ( > / = / < ) 0
− 4(
) ( > / = / < ) 0
2
(
)
)(
8
1
2 m
) − (
) m ( > / = / < ) 0
(
64
8
m ( > / = / < ) (
)
8
∴
m < 8
The range of possible values of m is (
).
+ 12x + 3m = 0 has a double real root.
2
8.
4x
Solution
+ 12 x + 3 m = 0 has a double real root.
Q The equation 4 x
2
∴ ∆ = 0
− 4(4)(3 m ) = 0
2
12
144 − 48 m = 0
m = 3
14
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