Question

Anna made an error in determining the polynomial equation of smallest degree whose roots are -4,-2, -

Answer 1

Answer:

See explanation

Step-by-step explanation:

Ana started the work nicely by multiplying out factors to get:\

$(x+4)(x+2)(2x+1)(x-2)=0$

She multiplied $(x+2)(x-2)$ correctly using difference of two squares to get: $x^2-4$

Unfortunately: She made a mistake in multiplying $(x+4)(2x+1)$ she mistakenly got $x^2+9x+4$ instead of $2x^2+9x+4$. She left out the coefficient of 2.

Therefore the second step should have been:

$(x^2-4)(2x^2+9x+4)$

The next step will now be:

$2x^4+9x^3+4x^2-8x^4-36x-16=0$

This simplifies to

$2x^4+9x^3-x^4-36x-16=0$