Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationGraph and Sign of QuadraticMedium2 minai-gemini

MathematicsMediumsingle choice

If the quadratic expression $a x^{2} + b x + c$ has the same sign as $a$ for all real $x$ , then:

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If a quadratic expression $a x^{2} + b x + c$ has the same sign as $a$ for all real $x$ , it means the parabola either lies entirely above the x-axis (if $a > 0$ ) or entirely below the x-axis (if $a < 0$ ). In either case, the quadratic equation $a x^{2} + b x + c = 0$ must have no real roots. This implies that its discriminant, $D = b^{2} - 4 a c$ , must be negative. Therefore, $b^{2} - 4 a c < 0$ .

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Graph and Sign of Quadratic

⏱ 2mℹ️ Source: ai-gemini

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