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प्रश्न
If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax2 +bx + 1 = 0 having real roots is
विकल्प
10
7
6
12
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उत्तर
Given that the equation `ax^2 +bx +1 = 0`.
For given equation to have real roots, discriminant (D) ≥ 0
⇒ b2 − 4a ≥ 0
⇒ b2 ≥ 4a
⇒ b ≥ 2√a
Now, it is given that a and b can take the values of 1, 2, 3 and 4.
The above condition b ≥ 2√a can be satisfied when
i) b = 4 and a = 1, 2, 3, 4
ii) b = 3 and a = 1, 2
iii) b = 2 and a = 1
So, there will be a maximum of 7 equations for the values of (a, b) = (1, 4), (2, 4), (3, 4), (4, 4), (1, 3), (2, 3) and (1, 2).
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