Quadratic EquationHard

Question

The possible value(s) of ' $p$ ' for which the equations $ax^{2} - px + ab = 0$ and $x^{2} - ax - bx + ab = 0$ may have a common root, given that $a,b$ are non zero real numbers is/ are :

Options

A.$b^{2} + a$
B.$a + ab$
C.$a^{2} + b$
D.$b + ab$

Solution

$x^{2} - ax - bx + ab = 0\ \Rightarrow \ x = a,b$

Put $x = a$ in $ax^{2} - px + ab = 0 \Rightarrow p = a^{2} + b$

Put $x = b$ in $ax^{2} - px + ab = 0 \Rightarrow p = a + ab$

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