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  4. The roots of ax2 + x + 1 = 0, where a ≠ 0 , are in the ratio 1: 1. Then a is equal to

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Q. The roots of $ax^2 + x + 1 = 0$, where $a \neq 0$ , are in the ratio $1 : 1$. Then a is equal to

KEAMKEAM 2017Complex Numbers and Quadratic Equations

Solution:

We have,
$a x^{2}+x+1=0$
Since, roots are in the ratio $1: 1$, thus roots are equal.
$\therefore $ Discriminant $=0$
$\Rightarrow (1)^{2}-4(a)(1)=0$
$\Rightarrow 1-4 a=0$
$\Rightarrow a=\frac{1}{4}$