Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsHard2 minQB

MathematicsHardsingle choice

Sum of the roots of the equation is $4^{x} - 3 (2^{x + 3}) + 128 = 0$

Answer:

Solution:

Put $2^{x} = y$ . Equation becomes $y^{2} - 3 (8 y) + 128 = 0 \Rightarrow y^{2} - 24 y + 128 = 0$

$\Rightarrow (y - 8) (y - 16) = 0 \Rightarrow y = 16, 8 \Rightarrow 2^{x} = 16, 8 \Rightarrow x = 4, 3$ ∴ Sum of the roots is 7 .

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Theory of equations

⏱ 2mℹ️ Source: QB

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