Question

Find all zeroes of F(x) = x2 -2x

Answer 1

ANSWER

2 and 0.

Step By Step Explanation

x² -2x

This is an quadratic equation with degree of 2 and can be solved by 3 different methods =>

1)Completing Square method.

2)Quadratic Formula method

3)Middle Term Split method.

Now,

1)Solving this equation by middle term Split method :>

x² - 2x = 0

=> x(x-2) = 0

So,

either x = 0

or x = 2

Hence 2 and 0 are roots of the given polynomial.

2) Solving this equation by quadratic formula method :>

d= b² - 4ac

=>d = (2)² - 4 (1)(0)

=> d = 4.

Now, we know that =>

x = $\dfrac{-b \pm \sqrt d}{2a}$

=>x = $\dfrac{2\pm \sqrt 4}{2 \times 1}$

=> x = $\dfrac{2\pm 2}{2}$

So,

either x = 0

or x = 2

Remember

-Discriminant decided the nature of roots.

- x = $\dfrac{-b \pm \sqrt d}{2a}$