Question

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots StartRoot 5 EndRoot and 2? 1) f (x) = 3 x cubed minus 6 x squared minus 15 x + 30
2)f (x) = x cubed minus 2 x squared minus 5 x + 10
3)f (x) = 3 x squared minus 21 x + 30
4) f (x) = x squared minus 7 x + 10

HURRY PLZ

Answer 1

Answer: 3

Step-by-step explanation:

Some important terms to be considered:

Degree of polynomial:

The highest power located at a particular variable(or sum of powers, if variables are in product form) of a particular term;

Suppose a polynomial:

f(x) = x²+ 2x + 2

Thus the degree of f(x) by above definition would.be 2 as it is the maximum power,

Another example:

g(x) = 2x³y² + 3x^4 + 6x²

The degree would be '5' , as by above definition, degree is the maximum power of a variable.or multiple variables in.product form(see term#1, power of x=3, power of y= 2, altogether , degree= 3+2=5.

Roots of the equation:

The particular values of the variables in an equation that satisfies(satisfaction indicates right side.to be equal to left side of the equation) that equation;

Example:

2x + y = 0;

Now we can say that x=1 anand y=-2 would the roots as they would generate 0 on L.H.S and that is equal to R.H.S.

That's it.

Now the demand is the polynomial of lowest degree that takes us to either option 3 or 4.

Now as the question demands a leading coefficient to be 3 that takes us to option 3 as there exists no such coefficient in 4. Now by putting the values 5 and 2 , the answer would be real obviously(as there would be no iota) and rational(in simple and suitable language, rational numbers are those that have an end, e.g 2.34356633325566... , would not be rational) too.