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Question

If the quadratic equation ax2+bx+6=0 does not have distinct real roots, then the least value of 2a+b is

A
2
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B
3
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C
6
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D
1
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Solution

The correct option is B 3
It is given that the expression ax2+bx+6=0 doesn't have distinct real roots.
The graph of the function doesn't cross the x-axis.
The expression f(x)=ax2+bx+6 is always greater than or equal to zero.
Hence, f(x)0.
f(2)=a(2)2+b(2)+60
4a+2b+60
2a+b+30
2a+b3

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