Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots startroot 5 endroot and 2?

Since there are two zeroes, the polynomial function of lowest degree is a quadratic polynomial.

Let it be p(x).

So,

Note that the leading coefficient should be 3.

Therefore,

Step-by-step explanation:

1) In this question we've been given "a", the leading coefficient. and two roots:

2) There's a theorem, called the Irrational Theorem Root that states:

If one root is in this form  then its conjugate . is also a root of this polynomial.

Therefore

3) So, applying this Theorem we can rewrite the equation, by factoring. Remembering that x is the root. Since the question wants it in this expanded form then:

f(x) = 3x² -21x + 30

Step-by-step explanation:

Polynomial function of lowest degree with roots as 'a' and 'b' and leading coefficient as 'c' is given by:

P(x) = c (x - a) (x - b)

Given: Leading coefficient = 3, Roots = sqrt 5 and 2

P(x) = 3 (x - 5) (x - 2)

      = 3 ( x² - 2x - 5x +10)

       = 3 ( x² - 7x +10)

       = 3x² - 21x + 30

Step-by-step explanation:

1) In this question we've been given "a", the leading coefficient. and two roots:

2) There's a theorem, called the Irrational Theorem Root that states:

If one root is in this form  then its conjugate . is also a root of this polynomial.

Therefore

3) So, applying this Theorem we can rewrite the equation, by factoring. Remembering that x is the root. Since the question wants it in this expanded form then:

the polynomial is:

Step-by-step explanation:

we know that the polynomial function p(x) of lowest degree with roots as 'a' and 'b' and leading coefficient as 'c' is given by:

here we are given that the roots are 5 and 2 and the leading coefficient is 3.

so the polynomial p(x) of lowest degree with the above properties is:

.

f(x) = 3x² -21x + 30

Step-by-step explanation:

Polynomial function of lowest degree with roots as 'a' and 'b' and leading coefficient as 'c' is given by:

P(x) = c (x - a) (x - b)

Given: Leading coefficient = 3, Roots = sqrt 5 and 2

P(x) = 3 (x - 5) (x - 2)

      = 3 ( x² - 2x - 5x +10)

       = 3 ( x² - 7x +10)

       = 3x² - 21x + 30

f(x) =

Step-by-step explanation:

If    is a root, then so is -

f(x) = 3(x + )(x - )(x - 2)

     =

     = 3()

     =

Since there are two zeroes, the polynomial function of lowest degree is a quadratic polynomial.

Let it be p(x).

So,

Note that the leading coefficient should be 3.

Therefore,