The gradient of the tangent to the curve

at the point (1, -2) is 1.

if the curve crosses the x-axis where x=2, find the values of p, q, and r. find the other point of intersection.

Because the curve crosses the -axis at , we know the point (2, 0) lies on the curve, so that

Tangents to the curve have slope :

and at the point (1, -2), the slope is 1, so that

This also tells us the point (1, -2) is on the curve, so that

Solve for ; you should get

so the equation of the curve is

Factorizing this yields

which means is a root and the curve intersects the -axis at the point (-1, 0).

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

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