Question

For what value of k the zeroes of x^2+kx+12 will differ by 1

Answer 1

We will use 2 formulas of quadratic equation to solve this question. one is sum of roots and the other product of roots.

We know that for equation
$a {x}^{2} + b {y}^{2} + c$
sum of roots is
$\binom{ - b}{a}$
and product of roots is
$\binom{c}{a}$
now coming to the question, let the roots be z and z+1

sum of roots =
$2z + 1 = - k$
product is
$(z)(z + 1) = 12$
solving the second equation we get z=3

and from the first equation k=-7

therefore we get our answer as
$k = - 7$