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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