Q.

If the equation ax2 + bx + c = 0 (a > 0) has two real roots α and β such that α<−2 and β>2, then which of the following statements is/are true?

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a

a−|b|+c<0

b

c<0,b2−4ac>0

c

4a−2|b|+c<0

d

9a−3|b|+c<0

answer is A.

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Detailed Solution

f(x)=ax2+bx+c    f(0)=c<0,D>0⇒     b2−4ac>0    f(1)<0 and f(−1)<0⇒     a−|b|+c<0    f(2)<0 and f(−2)<0⇒     4a−2|b|+c<0Nothing can be said about f(3) or f(-3), whether it is positive or negative.
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If the equation ax2 + bx + c = 0 (a > 0) has two real roots α and β such that α<−2 and β>2, then which of the following statements is/are true?