If f(x) = ax2 + bx + c, where a, b, c ∈ R and a < 0, such that ax2 + bx + c = 0 does not have any real roots then
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If f(x) = ax2 + bx + c, where a, b, c ∈ R and a < 0, such that ax2 + bx + c = 0 does not have any real roots then
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Answer:
Consider the equation,
ax
2
+bx+c
Now if b
2
−4ac<0, then it does not have any real roots and hence it will not intersect the x axis at any point.
If a>0 then y=ax
2
+bx+c will lie completely above x axis and
If a<0 then y=ax
2
+bx+c will lie completely below x axis.
It is given that the above equation is always greater than zero,
Or
ax
2
+bx+c>0 for ϵR.
This can only occur is
b
2
−4ac<0 and a>0.
my self shreya,,,,,
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