Roots of Polynomials

Given this graph of a 3rd degree polynomial, what type of roots does the polynomial have?

• Three real

• One real, and two imaginary

• Two real, and one imaginary

• Three imaginary

Which of the following would be the correct factored form of a 4th degree polynomial with with roots 2, 5i, and 6?

• (x-6)(x-2)(x+5i)(x-5i)

• (x+6)(x+2)(x+5i)

• (x-6)(x-2)(x-5i)

• (x+6)(x+2)(x-5i)

Tags

CCSS.HSA.APR.B.3

What is the factored form of the function graphed?

• y = -(x+6)(x-5)(x-8)

• y = -(x-6)(x+5)(x+8)

• y = -(x-5)(x-8)

• y = -(x+6)(x-5)

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.APR.B.2

CCSS.HSA.REI.D.11

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which of the following would be a root with 3i?

• 3i²

• -3i

• 3i

• -3i²

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

What are the roots of the polynomial  $h\left(x\right)=\left(x-3\right)\left(x+2\right)\left(2x+1\right)$ ?

• -3,2,1

• 3,-2,-1

• 3,-2, $-\frac{1}{2}$  

• -3,2, $\frac{1}{2}$  

Tags

CCSS.HSF-IF.C.7C

 The sum of squares will always give you 2 non-real roots.    $x^2+49=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^2=-49\ \ \ \ \ \ \ \ \ \ \ x=\pm\sqrt{49}\sqrt{-1}$ Which are equivalent solutions for the roots of this polynomial? Check all that are true.

•  $\pm7i$  

•  $7\sqrt{-1},\ -7\sqrt{-1}$  

•  $\pm7\sqrt{-1}$  

•  $7i\ \ ,\ -7i$  

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

What are the roots of the polynomial
 $f\left(x\right)=\left(x^2-16\right)\left(x^2+25\right)\left(x+3\right)$  

• 4,-4,5i,-5i,-3

• 4i,-4i,5,-5,-3

• 4,-4,5,-5,-3

• 4,-4,5i,-5i,3

Tags

CCSS.HSF-IF.C.7C

What is another way to say "where a function crosses the x-axis"?

• x-intercept

• zero

• root

• all of these.

Tags

CCSS.HSF-IF.C.7C

How could you determine    if x-2 is a factor of 2x³-5x²+x-2?

• Use synthetic division and see if the quotient is even
• Ask the person sitting next to me
• Use synthetic division and see if the remainder is zero
• Flip a coin

Tags

CCSS.HSA.APR.D.6

If a zero of a polynomial function has multiplicity 4 that means:

• The x intercept is at (4, 0)

• The graph will "touch" at that zero

• The graph will "pass through" at that zero

• Zeros cannot have multiplicity of 4