Question

Two numbers whose sum is $6$ and the absolute value of whose difference is $8$ are the roots of the equation:

• A. $a^2-6a+7=0$
• B. $a^2-6a-7=0$
• C. $a^2-6a-8=0$
• D. $a^2-6a+8=0$

Answer 1

Answer: (B)

$a^2-6a-7=0$

Let roots of equation be $p$ and $q$

$\therefore$ Equation is $a^2-(p+q)a+pq=0$

Given that,

$p+q=\mathrm{6....}\left(1\right)$

$|p-q|=\mathrm{8....}\left(2\right)$

Squaring and adding both the equations, we get

$2(p^2+q^2)=100$

$\Rightarrow p^2+q^2=50$

Squaring equation $\left(1\right)$, we get

$p^2+q^2+2pq=36$

$\Rightarrow pq=-7$

$\therefore$ Equation is $a^2-6a-7=0$