Question

FX equal to X square + bx + c has no real zeros and a + b + c less than zero then

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If f(x) = ax² + bx + c has no real zeros and a + b + c < 0 then

a) c = 0

b) c > 0

c) c < 0

d) None of the above

EVALUATION

Here the given function is

f(x) = ax² + bx + c

Since it is a polynomial

So f(x) is continuous

Since f(x) = ax² + bx + c has no real zeros

So f(x) ≠ 0 for all x ∈ R

Either f(x) < 0 or f(x) > 0 for all x ∈ R

Now f(1) = a + b + c

Since a + b + c < 0

∴ f(1) < 0

By the continuity of f(x) we have

f(x) < 0 for all x ∈ R

Then f(0) < 0

⇒ 0 + 0 + c < 0

⇒ c < 0

FINAL ANSWER

Hence the correct option is c) c < 0

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