Can a cubic equation have only one real root?

Can a cubic equation have only one real root?

Cubic equations and the nature of their roots Just as a quadratic equation may have two real roots, so a cubic equation has possibly three. But unlike a quadratic equation which may have no real solution, a cubic equation always has at least one real root. We will see why this is the case later.

How do you find the cubic equation when given the roots and Y intercept?

Starts here3:40Find Cubic Polynomial Function From Given Roots and Y InterceptYouTubeStart of suggested clipEnd of suggested clip55 second suggested clipWe are looking for a cubic function so cubic function means what we have now three zeros. So weMoreWe are looking for a cubic function so cubic function means what we have now three zeros. So we could write this cubic function as f of x equals to a times X minus 2 this is because of that 0.

How do you find a cubic function with given roots?

Approach: Let the root of the cubic equation (ax3 + bx2 + cx + d = 0) be A, B and C. Then the given cubic equation can be represents as: ax3 + bx2 + cx + d = x3 – (A + B + C)x2 + (AB + BC +CA)x + A*B*C = 0. Therefore using the above relation find the value of X, Y, and Z and form the required cubic equation.

How do you show a cubic only one root?

Starts here9:54Exam Problem: Cubic Polynomial w/ 1 Real Root – YouTubeYouTubeStart of suggested clipEnd of suggested clip61 second suggested clipIf you get this maximum. Here okay and if you get the maximum. Below the axis y is less than zero.MoreIf you get this maximum. Here okay and if you get the maximum. Below the axis y is less than zero. In the same way your home and host. Okay. So how do i get these stationary.

Why do cubic equations have at least one real root?

Only the sign of the imaginary component has changed, which equals 0. So if z is a zero, so is ¯z. As a polynomial has a number of zeroes equals to its degree, a cubic has at least one real root.

Why cubic equation has at least one real root?

First, if r is a root of a polynomial with real coefficients, then its complex conjugate is also a root. So the non-real roots, if any, occur as pairs of complex conjugate roots. As a cubic polynomial has three roots (not necessarily distinct) by the fundamental theorem of algebra, at least one root must be real.

How do you find the Y intercept of a cubic function?

Y-Intercept of Cubic Function A cubic function always has exactly one y-intercept. To find the y-intercept of a cubic function, we just substitute x = 0 and solve for y-value. Example: To find the y-intercept of f(x) = x3 – 4×2 + x – 4, substitute x = 0. Then f(x) = 03 – 4(0)2 + (0) – 4 = -4.

How do you write the cubic function in intercept form?

Starts here2:09Writing a Cubic Function Given Zeros – YouTubeYouTube

Why do all cubic functions have to have at least one root?

It’s not completely accurate that every cubic polynomial has one real root: the cubic equation has no real solutions. However, if the coefficients of the cubic polynomial are real numbers, then it is indeed the case that the polynomial must have at least one real root.

How do you show a root is the only real root?

Starts here6:55Prove the equation has at least one real root (KristaKingMath) – YouTubeYouTube