A simple subtraction

Algebra Level 2

The equation x 2 + 13 x − 168 = 0 x^{2} + 13x - 168 = 0 has 2 real roots. Let the larger root be a and the smaller root be b.

Find a - b


The answer is 29.

Denton Young by Denton Young , 47, USA

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2 solutions

Denton Young
Jul 18, 2015

The equation factors as ( x − 8 ) ( x + 21 ) = 0 (x-8)(x+21) = 0

So x = 8 or x = -21

8 - (-21) = 29

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Bala Vidyadharan
Jul 19, 2015

Also learn the other way of doing this sum ,when the coefficients are in terms of variables

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

a+b=-13, ab=-168 Now the required one is a-b

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

(a-b)^2=(-13)^2-4(-168)

(a-b)^2=841

(a-b)=29

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