Find out the answer to "You are given a quadratic equation of the..."

Painevg

Answered question

2021-12-06

You are given a quadratic equation of the form

(x - p) (x - q) = 0

Show that the axis of symmetry of the related quadratic function is equidistant from the roots p and q.

Pademagk71

Beginner2021-12-07Added 34 answers

Step 1

(x - p) (x - q) = 0

x^{2} - x q - p x + p x + p q = 0

x^{2} + (- q - p) x + p q = q

Axis of symmetry of

y = a x^{2} + b x + c

x = \frac{- b}{2 a}

Axis of symmetry is

x = \frac{- (- q - p)}{2 (1)}

Let

x_{1} = x = \frac{p + q}{2}

x_{2} = x = p

x_{3} = q

Distance between

x_{2}

and

x_{1}

| x_{2} - x_{1} | = | p - (\frac{p + q}{2}) | = | \frac{p - q}{2} | = \frac{p - q}{2}

Step 2
Distance between

x_{3}

and

x_{1}

| x_{3} - x_{1} | = | q - (\frac{p + q}{2}) | = | \frac{q - p}{2} | = | \frac{- (p - q)}{2} |

= \frac{p - q}{2}

∴

The axis of symmetry is equidistant from the roots p and q

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