if the discriminant of a quadratic equation is 4, which statement describes the roots?

A) There are two complex roots.
B) There are two real roots.
C) There is one real root.
D) There is one complex root

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For what values of c does the polynomial have two inflection points? One inflection point? None? Illustrate by graphing P for several values of c. How does the graph change as c decreases?

Tynup Solution:

Given:

Differentiating

For c ≠ 0, there are two distinct roots for the equation.

Hence, for two inflection points the required condition is.

When c = 0, there is only one root for the equation.

Hence, when c = 0, the function has one inflection point.

Recall that the quadratic equation does not have real roots if its Discrimnant is less than zero.

Hence, for no inflection points

, which is not possible.

Hence, the polynomial function has minimum of one inflection point.

For different values of c

The common inflection point is (0, 0) and other inflection point is,

Hence,

On decreasing the value of c, the inflection point moves towards positive quadrant.

amaranthmule534

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if the discriminant of a quadratic equation is 4, which statement describes the roots? A) There are two complex roots.B) There are two real roots.C) There is one real root.D) There is one complex root

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if the discriminant of a quadratic equation is 4, which statement describes the roots?

A) There are two complex roots.
B) There are two real roots.
C) There is one real root.
D) There is one complex root