x^2 - 11x + a and x^2 - 14x + 2awill have a common factor, if a = - Vidyadip

MCQ

${x^2} - 11x + a$ and ${x^2} - 14x + 2a$will have a common factor, if $a = $

A
$24$
✓
$0, 24$
C
$3, 24$
D
$0, 3$

✓

Answer

Correct option: B.

$0, 24$

b
(b) Expressions are ${x^2} - 11x + a$ and ${x^2} - 14x + 2a$ will have a common factor, then

$ \Rightarrow \,\,\frac{{{x^2}}}{{ - 22a + 14a}} = \frac{x}{{a - 2a}} = \frac{1}{{ - 14 + 11}}$

$⇒$ $\frac{{{x^2}}}{{ - 8a}} = \frac{x}{{ - a}} = \frac{1}{{ - 3}}$$⇒$ ${x^2} = \frac{{8a}}{3}$ and $x = \frac{a}{3}$

$⇒$ ${\left( {\frac{a}{3}} \right)^2} = \frac{{8a}}{3}\,\,\,\, \Rightarrow \frac{{{a^2}}}{9} = \frac{{8a}}{3}$ $⇒$ $a = 0,\,\,24$.

Trick : We can check by putting the values of a from the options.

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