If the difference of the roots of the quadratic equation $x^2 + k x + 12 = 0$ is 1 , what is the positive value of k ?

Given :

Given equation is $x^2 + k x + 12 = 0$

The difference of the roots of the given quadratic equation is 1.

To do :

We have to find the positive value of k.

Solution :

Let a, b be the roots of the given equation.

This implies,

Sum of the roots $= a+b = \frac{-k}{1} = -k$

Product of the roots $= ab = \frac{12}{1} = 12$

Difference of the roots $= a-b = 1$

Squaring on both sides,

$(a-b)^2 = 1^2$

$a^2 + b^2 - 2 a b = 1$ 

$(a+b)^2 - 4ab = 1$

$(-k)^2 -4(12) = 1$

$k^2 = 1+48$

$k^2 = 49$

$k = 7 or -7$

Therefore, the positive value of k is $7$.

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Updated on: 10-Oct-2022

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