# Does the curve 2x^2=10 have x intercepts?

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The two answers above show how to find the x-intercepts through factoring. You could also find them using the quadratic formula and by graphing.

Method 1. Quadratic Formula

2x^2=10

2x^2 - 10 = 0

2x^2 + 0x + -10 = 0

a = 2, b = 0, c = -10

x = [-b `+-` sqrt(b^2 - 4ac)] / 2a

x = [-0 `+-` sqrt(0^2 - 4*2*-10)] / 2*2

x =`+-` sqrt(80) / 4

x = `+-` 4sqrt(5) / 4

**x = `+-` sqrt(5)**

Method 2: Graphing

2x^2=10

2x^2 - 10 = 0

Graph y = 2x^2 - 10

**The x-intercepts are `+-` sqrt(5).**

The curve 2x^2 = 10 intercepts the x-axis if the equation 2x^2 - 10 = 0 has real roots

2x^2 - 10 = 0

=> 2(x^2 - 5) = 0

=> x^2 = 5

=> x = sqrt 5 and -sqrt 5

**The curve intersects the x-axis at the points (sqrt 5, 0) and (-sqrt 5, 0)**

To determine the intercepting points of the given curve to x axis, you'll have to set y = 0.

y = 2x^2 - 10

2x^2 - 10 = 0

We'll divide by 2:

x^2 - 5 = 0

x^2= 5

x1 = +sqrt5 and x2 = -sqrt5

**The x intercepts of the given curve are (sqrt5 ; 0) and (-sqrt5 ; 0).**