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

Correct option is 1,2,3undefined

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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?

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a−|b|+c<0

c<0,b2−4ac>0

4a−2|b|+c<0

9a−3|b|+c<0

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detailed solution

Correct option is A

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?

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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?