$\left( a^{2} - 3a + 2 \right)x^{2} + \left( a^{2} - 5a + 6 \right)x + a - 2 = r$ for three distinct values of $x$ for some $r \in R,\ if$ $a + r$ is equal to

Question

Dr. Abubacker · Accepted Answer

(b)
Now, $a^{2} - 3a + 2 = 0$
$\Rightarrow a = 1,\ 2$ …(i)
and $a^{2} - 5a + 6 = 0$
$\Rightarrow a = 2\ ,3$ ...(ii)
$\Rightarrow a - 2 - r = 0$
At $a = 2$ [common value from Eqs. (i) and (ii)]
$r = 0$
So, $a + r = 2$

Q. $\left( a^{2} - 3a + 2 \right)x^{2} + \left( a^{2} - 5a + 6 \right)x + a - 2 = r$ for three distinct values of $x$ for some $r \in R,\ if$ $a + r$ is equal to

Explanation

Reviewed by Dr. Abubacker

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