Question

if one of the zeros of the cubic polynomial ax3 + bx2 + cx + d is 0 , find the product of other two zeros

Answer 1

Answer:

Let p(x) =ax3 + bx2 + cx + d

Given that, one of the zeroes of the cubic polynomial p(x) is zero.

Let α, β and γ are the zeroes of cubic polynomial p(x), where α = 0.

We know that,

Step-by-step explanation:

sum of two zeros at a time = c/a

                      ∴αβ + βy + yα = c/a

                  ∴0×β + βy + y×0 = c/a

                                         βy = c/a

  hence, product of 2 zeros = c/a

Hope, it helped you ............... : )

Answer 2

Answer:

c/a

Step-by-step explanation:

Given, the cubic polynomial is ax³ + bx² + cx + d.

One of the zeros of the polynomial is zero.

We know that, if m , n and p are the zeroes of a cubic polynomial ax³ + bx² + cx + d, then

m + n + p = -b/a

mn + np + pm = c/a

mnp = -d/a

given, m= 0

Now, mn + np + pm = (0)n + np + p(0) = np

By using the property of polynomials,

np = c/a

Therefore, the product of the other two roots is c/a.