An algebra problem by Achal Jain

Algebra Level 4

Let $\alpha$ and $\beta$ be the roots of the polynomial $(x-a)(x-b)-c$ with $c \neq 0$ . Then what the zeroes of the polynomial $(x-\alpha)(x-\beta) +c$ ?

c,b

a,c

a-c,b-c

a+c,b+c

a,b

1 solution

Achal Jain
Apr 3, 2017

After opening the first polynomial we get

$x^{2}-x(a+b) +ab-c$ and $\alpha, \beta$ are the roots $\therefore$ $\alpha+\beta= a+b$ and $\alpha \times \beta =ab-c$

Then after opening the second polynomial

$x^{2}-x(\alpha+\beta)$ + $\alpha \beta +c$ then after substituting the values obtained from the first polynomial

The equation transforms to $x^{2}-(a+b)+ab$ .

Thus we get the roots as $a,b$

An algebra problem by Achal Jain

1 solution

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