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if the equation ax 2 + bx + c = 0 does not have 2 distinct real roots and a + b > c, then prove that f(x) >=0, for all view x belongs to R.

if the equation ax2+ bx + c = 0 does not have 2 distinct real roots and a + b > c, then prove that f(x) >=0, for all view x belongs to R.

Grade:12

1 Answers

Vikas TU
14149 Points
5 years ago
if the equation ax2+ bx + c = 0 does not have 2 distinct real roots
then its D
b^2 – 4ac
b^2
for the condition to b true,
a and c should both be positive or both should be negative.
But as we know for f(x) >=0
only the condition holds for true is:
a>0 and c >0.
hence, f(x) >=0

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