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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
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Asked by acshanadhana15 | 14 Oct, 2020, 02:33: PM
answered-by-expert 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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