First slide

Theory of equations

Question

if $1 - p$ is a root of the quadratic equation
$x^{2} + p x + 1 - p = 0$ then its roots are

Moderate

A

0, 1
B

–1, 1
C

0, – 1
D

–2, 1

Solution

$(1 - p)^{2} + p (1 - p) + (1 - p) = 0$
$\begin{array}{l} \Rightarrow (1 - p) [1 - p + p + 1] = 0 \Rightarrow 2 (1 - p) = 0 \\ \Rightarrow p = 1 \end{array}$
Thus, equation becomes $x^{2} + x = 0$
$x = 0 or - 1$

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