Find the co-ordinates where the curve y= 2x^2 + 7x + 3 crosses the x axis

At the x axis, y = 0 so the equation can be made equal to zero. For a polynomial of the form ax^2 + bx + c = 0, find the value of ac. E.G ac is 2*3 = 6. Determine the two numbers which give a sum equal to b and a product equal to ac. E.G b = 7 and ac = 6, in this case this gives 6 and 1. Separate the quadratic into two parts to factorise, by splitting the 7x into 6x and 1x, as this satisfies the above condition. 2x^2 + 6x + x + 3 = 0. Factorise by: 2x(x + 3) + 1(x + 3) = 0, which gives (2x+1) (x+3) = 0. The roots are the points where the curve crosses the x axis, and can be found by determining values of x which satisfy the above equation. To make the whole equation equal zero, it is easier to approach each bracket and make that equal 0. 2x + 1 = 0 so 2x = -1 which gives x = -1/2 and x + 3 = 0 so x = -3. The curve crosses the x axis at the points (-1/2,0) and (-3,0).