Algebra maximum number of roots

Question

Find the maximum number of roots of P(x) = 2x² + 14x - 7.
Question options:

a) 1

b) 2

c) 3

d) 4

 

Please explain how to find the maximum number of roots.

Answer 1

Carl F. Gauss proved that a polynomial of degree n has exactly n roots, in the Complex set of numbers (of which Reals are a subset).  A double root counts as 2 roots under this scheme.

 

For a quadratic function (n = 2), the graph is a parabola. It can

• cross the x-axis twice ⇐the case where there are two real zeros; discriminant > 0
• it can merely be tangent to the x-axis ⇐the case of one real 'double' root; discriminant = 0
• it can open upwardly but have vertex above the x-axis ⇐the case where there are two complex conjugate roots; discriminant < 0.

The 'discriminant' is that part of the quadratic formula appearing under the square root symbol (b²-4ac)