TMUA Juan Set 2 Paper 1 · Question 7

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Juan Set 2 Paper 1 · Q7

Paper 1Algebra

Let $a$ and $b$ be positive real numbers such that for each of the equations

ax^2-2x+b=0,\qquad bx^2-3bx+a=0

the sum of the roots is 1 more than the product of the roots.

Which of the following could be the second-degree equation whose roots are $a$ and $b$ ?

9x^2+8x+18=0

9x^2-14x+8=0

9x^2-18x+14=0

9x^2-8x+14=0

9x^2-18x+8=0

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