CBSE Class 10 Answered
If a and b can take values 1,2,3,4 .Then the number of the equations of the form ax^2+bx+1= 0 having real roots is
10
7
6
12
Asked by acshanadhana15 | 14 Oct, 2020, 02:33: PM
Expert Answer
To have real roots of equation ax2 + bx +1 = 0 , we should have the condition (b2 - 4 a) ≥ 0 .
Following tables gives the value of ( b2 - 4 a ) for different values of a and b with in the range 1,2,3,4
a | b | b^2 - 4a |
1 | 1 | -3 |
1 | 2 | 0 |
1 | 3 | 5 |
1 | 4 | 12 |
2 | 1 | -7 |
2 | 2 | -4 |
2 | 3 | 1 |
2 | 4 | 8 |
3 | 1 | -11 |
3 | 2 | -8 |
3 | 3 | -3 |
3 | 4 | 4 |
4 | 1 | -15 |
4 | 2 | -12 |
4 | 3 | -7 |
4 | 4 | 0 |
From above table we see only 7 combination of a and b satisfies the condition (b2 - 4 a) ≥ 0 .
Hence we get 7 equations that have real roots.
Answered by Thiyagarajan K | 14 Oct, 2020, 08:22: PM
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