Write a polynomial f(x) that meets the given conditions. Answers may very

Mathematics

1 answer:

AnnZ [28]3 years ago

4 0

The polynomial is: $f(x)=x^3-2x^2-23x+60$

Step-by-step explanation:

We need to write a polynomial f(x) that meets the given conditions: Degree 3 polynomial with zeros 3,-5,4

Since zeros are at 3,-5 and 4

So, x=3, x=-5 and x=4

or:

x-3=0, x+5=0 and x-4=0

Multiplying all factors to find the polynomial:

$(x-3)(x+5)(x-4)=0\\(x(x+5)-3(x+5))(x-4)=0\\(x^2+5x-3x-15)(x-4)=0\\(x^2+2x-15)(x-4)=0\\x(x^2+2x-15)-4(x^2+2x-15)=0\\x^3+2x^2-15x-4x^2-8x+60=0\\x^3+2x^2-4x^2-15x-8x+60=0\\x^3-2x^2-23x+60=0$

So, the polynomial is: $f(x)=x^3-2x^2-23x+60$

keywords: Factors and zeros of polynomial

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3 years ago

Prove that: –7 is not the arithmetic square root of 49

frez [133]

Answer:

–7 is not the arithmetic square root of 49 only in case we are taking it for natural number.

Step-by-step explanation:

The square root of x is that number which on squaring gives the result as x.
For example, the square root of 4 is +2 or -2. Because on squaring +2 or -2 we get the number 4.
Similarly for the case of 49, the square root might be both +7 or -7.
But if we are taking it as a natural number then -7 is not valid. Like for length, quantity or other sort of things -7 is not the arithmetic square root of 49.