Q.

If f(x)=ax2+bx+c, where a≠0,b,c∈R, then which of the following conditions implies that f(x) has real roots?

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a

a + b + c = 0

b

a and c are of opposite signs

c

4ac−b2<0

d

a and b are of opposite signs

answer is A.

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Detailed Solution

(1) If f(1)=0⇒a+b+c=0So, roots are real.(2) D=b2−4acIf ac<0⇒D>0So, roots are real.(3) 4ac−b2<0⇒b2−4ac>0So, roots are real.(4) This is not the sufficient condition.
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If f(x)=ax2+bx+c, where a≠0,b,c∈R, then which of the following conditions implies that f(x) has real roots?