taiwan-gsat 2022 Q12

taiwan-gsat · Other · gsat__math-b 5 marks Solving quadratics and applications Finding roots or coefficients of a quadratic using Vieta's relations

Let $a, b, c$ be nonzero real numbers, and the two roots of the quadratic equation $ax^2 + bx + c = 0$ both lie between 1 and 3. Select the equation whose two roots must lie between 4 and 5.
(1) $a(x-2)^2 + b(x-2) + c = 0$
(2) $a(x+2)^2 + b(x+2) + c = 0$
(3) $a(2x-7)^2 + b(2x-7) + c = 0$
(4) $a\left(\frac{x+7}{2}\right)^2 + b\left(\frac{x+7}{2}\right) + c = 0$
(5) $a(3x-11)^2 + b(3x-11) + c = 0$

Let $a, b, c$ be nonzero real numbers, and the two roots of the quadratic equation $ax^2 + bx + c = 0$ both lie between 1 and 3. Select the equation whose two roots must lie between 4 and 5.\\
(1) $a(x-2)^2 + b(x-2) + c = 0$\\
(2) $a(x+2)^2 + b(x+2) + c = 0$\\
(3) $a(2x-7)^2 + b(2x-7) + c = 0$\\
(4) $a\left(\frac{x+7}{2}\right)^2 + b\left(\frac{x+7}{2}\right) + c = 0$\\
(5) $a(3x-11)^2 + b(3x-11) + c = 0$

Paper Questions

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