Question

The curves $y=x^2+9x+20$ and $y=x^2+bx+c$ intersect the $X$-axis at the points $\left({\alpha }_i,0\right),(i=1,2,3,4)$. If ${\alpha }_1<{\alpha }_2<{\alpha }_3<{\alpha }_4$ be such that $\left|{\alpha }_1-{\alpha }_3\right|=\left|{\alpha }_2-{\alpha }_4\right|=8$, then the sum of all possible values of $b$ and $c$ is

• A. 186
• B. 159
• C. 216
• D. None of the above

Answer 1

Answer: (D)

The roots of quadratic equation
$x^2+9x+20=0$ are $-4$ and $-5$
So, the possible roots of quadratic equation
$x^2+bx+c=0$ are according to given information
$\left(x_1,x_2\right)=(-13,4),(3,4),(-13,-12)$
$\therefore$ Possible values of $b$ are $9,-7,25$
and possible values of $c$ are $-52,12,156$
therefore sum of all possible value of $b$ and $c$ is
$9-7+25-52+12+156=143$