If f x - a x square plus b x plus c has no real zeros and a - b - c 0C c -0D none of these

Since f(x)≠0 for x∈R, either f(x) gt;0 for all x∈R or f(x) lt;0 for all x∈R by continuity of f. Since f(1)=a+b+c lt;0, we conclude that f(x) lt;0 for al ...

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Byju's Answer

Standard IX

Mathematics

Zeroes of a Polynomial

If f x = a x ...

Question

If f(x)= a x square plus b x plus c has no real zeros and a+b+c <0 , then
A) c=0
B) c>0
C) c<0
D) none of these

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Solution

Since f(x)≠0 for x∈R, either f(x)>0 for all x∈R or f(x)<0 for all x∈R by continuity of f.

Since f(1)=a+b+c<0, we conclude that f(x)<0 for all x∈R. Therefore f(0)=c<0.

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If f(x)= a x square plus b x plus c has no real zeros and a+b+c <0 , then A) c=0 B) c>0 C) c<0 D) none of these

Since f(x)≠0 for x∈R, either f(x)>0 for all x∈R or f(x)<0 for all x∈R by continuity of f. Since f(1)=a+b+c<0, we conclude that f(x)<0 for all x∈R. Therefore f(0)=c<0.

If f(x)= a x square plus b x plus c has no real zeros and a+b+c <0 , then
A) c=0
B) c>0
C) c<0
D) none of these

Since f(x)≠0 for x∈R, either f(x)>0 for all x∈R or f(x)<0 for all x∈R by continuity of f.

Since f(1)=a+b+c<0, we conclude that f(x)<0 for all x∈R. Therefore f(0)=c<0.