Chapter 1 Quadratic Equations In One Unknown Worksheet With Answers Page 15
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Quadratic Equations in One Unknown
− 4x + 16 = 0 has no real roots.
2
9.
mx
Solution
− 4 x + 16 = 0 has no real roots.
Q The equation mx
2
∴ ∆ < 0
− 4( m )(16) < 0
2
(−4)
16 − 64 m < 0
1
m >
4
1
∴ The range of possible values of m is m >
.
4
+ mx + 1 = 0 has a double real root.
2
10. 25x
Solution
+ mx + 1 = 0 has a double real root.
Q The equation 25 x
2
∴ ∆ = 0
− 4(25)(1) = 0
2
m
− 100 = 0
2
m
= 100
2
m
or m = −10
m = 10
− 14x + m = 0 has real roots.
2
11. 36x
Solution
− 14 x + m = 0 has real roots.
Q The equation 36 x
2
∴ ∆ ≥ 0
− 4(36)( m ) ≥ 0
2
(−14)
196 − 144 m ≥ 0
49
m ≤
36
49
∴ The range of possible values of m is m ≤
.
36
15
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