Polynomial Problems

Polynomial Problems

**Page 1**

1.

z = 2 - 3i is 1 root of $z^3 - pz^2 + qz - r = 0$ and p,r and q are real. Find the real root in terms of p and r?

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2.

If p,q,r and s are real numbers such that pr = (q+s), then show that atleast one of the equations $x^2$+px+q = 0 and $x^2$+rx+s = 0 has real roots.

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3.

How to find all rational zeros?

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4.

In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend?

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5.

Use given zero to find the remaining zeros of the polynomial

g(x)=$2x^5-3x^4-5x^3-15x^2-207x-108$

Given zero: 3i

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6.

Ned needs to ship six identical packages, each weighing 3 lb 12 oz. What is the total weight of the shipment?

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7.

Ned needs to ship six identical packages, each weighing 3 lb 12 oz. What is the total weight of the shipment?

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8.

If x is 1/5 of y, y is 3/10 of z, and z > 0, then x is what fraction of z?

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9.

What is the difference between synthetic division and synthetic substitution?

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10.

What is 'extreme values of a polynomial'?

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