For how many diff erent values of a does following system have at least two distinct solutions? a x+

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3 and 4 .Determinants and Matrices

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For how many diff erent values of $a$ does the following system have at least two distinct solutions?

$a x+y=0$

$x+(a+10) y=0$

A

$0$

B

$1$

C

$2$

D

Infinitely many

(KVPY-2017)

Solution

(c)

We have, $a x+y=0$

$x+(a+10) y=0$

From Eqs.$(i)$ and $(ii)$, we get

$\frac{a}{1}=\frac{1}{a+10} \Rightarrow a^2+10 a-1=0$

$a=\frac{-10 \pm \sqrt{104}}{2}$

$\therefore$ Two values of $a$ for systems has at least two distinct solution.

Standard 12

Mathematics

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