Question

x,x-4,x+5 are the factors of the left hand side of the equation
a) x^3+2x^2-x-2=0
b)x^3+x^2-20x=0
c)x^3-3x^2-4x+12=0
d)x^3-6x^2+11x-6=0

Answer 1

Answer:

b) x^3 + x^2 - 20x is the correct answer

Answer 2

Given:

x, x-4, x+5 are the factors of the equation.

To Find:

Which equation have the factor x,x-4,x+5 ?

Solution:

Let equation is P(x), then P(x) can be written as:

$\mathbf{P(x)=x\times (x-4)\times (x+5)}$

$\mathbf{P(x)=x\times \left (x ^{2}+(-4+5)x+(-4)(+5) \right )}$

$\mathbf{P(x)=x\times \left (x ^{2}+(1)x+(-20) \right )}$

$\mathbf{P(x)=x\times (x ^{2}+x-20)}$

$\mathbf{P(x)= x ^{3}+x^{2}-20x}$

But P(x) is an equation,so:

P(x) = 0

Means:

$\mathbf{P(x)= x ^{3}+x^{2}-20x=0}$

$\mathbf{x ^{3}+x^{2}-20x=0}$

Means option B is correct.