Question

The graph of the polynomial p(x) = x^5+ ax^4 + bx^3+ cx^2+ dx+ e has five distinct x-intercepts, one of which is at (0, 0). Which of the following
coefficients cannot be zero?
a. b
b.d
c.a
d. c​

Answer 1

Answer:

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Step-by-step explanation:

MATHS

The graph of the polynomial P(x)=x

5

+ax

4

+bx

3

+cx

2

+dx+e has five distinct x−intercepts, one of which is at (0,0). Which of the following coefficients cannot be zero ?

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VIDEO EXPLANATION

ANSWER

Since P(0)=0, we have e=0 and

P(x)=x(x

4

+ax

3

+bx

2

+c+d).

Suppose that the for, remaining x−intercepts are at p,q,r and s.

Then x

4

+ax

3

+bx

2

+cx+d

=(x−p)(x−q)(x−r)(x−s). and d=pqrs



=0

Any of the other constants could be zero.

For example consider

P

1

(x)=x

5

−5x

3

+4x=x(x+2)(x+1)(x−1)(x−2)

and P

2

(x)=x

5

−5x

4

+20x

2

−16x=x(x+2)(x−1)(x−2)(x−4)