How do you know how many roots a quadratic equation has?
To work out the number of roots a qudratic ax2+bx+c=0 you need to compute the discriminant (b2-4ac).
If the discrimant is less than 0, then the quadratic has no real roots.
If the discriminant is equal to zero then the quadratic has equal roosts.
If the discriminant is more than zero then it has 2 distinct roots.
LC
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Consider the functions f(x) = −x^3 + 2x^2 + 3x and g(x) = −x^3 + 3x^2 − x + 3. (a) Find df/dx (x) and hence show that f(x) has turning points at when x = 2 /3 ± √ 13/ 3 . [5] (b) Find the points where f(x) and g(x) intersect. [4]