14.01.2020

# Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots startroot 5 endroot and 2? 17

17.02.2022, solved by verified expert
49 students found this answer helpful Or Step-by-step explanation:

For a polynomial function of lowest degree with rational real coefficients, each root has multiplicity of 1.

The polynomial has roots and 2 with a leading coefficient of 3.

By the irrational root theorem of polynomials, is also a root of the required polynomial.

By the factor theorem, we can write the polynomial in factored form as: We expand, applying difference of two squares to obtain We expand further using the distributive property to get: ### Faq

Mathematics 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: Mathematics

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

Mathematics

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,   Mathematics
The polynomial functions A) and C) have a leading coefficient of 3, but C) has a lower degree.
f ( x ) = 3 x² - 21 x + 30
3 ( x² - 7 x + 10 ) = 3 ( x² - 5 x - 2 x + 10 ) =
= 3 ( x ( x - 5 ) - 2 ( x - 5 )) = 3 ( x - 2 ) ( x - 5 ) = 0
x = 2 and x = 5 ( roots )

C ) f ( x ) = 3 x² - 21 x + 30
Mathematics

f(x) = Step-by-step explanation:

If is a root, then so is - f(x) = 3(x + )(x - )(x - 2)

= = 3( )

= Mathematics 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: Mathematics
We are asked in the problem to determine the polynomial function with a leading coeffiient of 3 and whose roots are square root of 5 and 2. In this case, the poolynomial function becomes:

(x-√5) (x-2) = x^2 - 2(2+√5) + 2√5
(x^2 - 2(2+√5) + 2√5)*3 = 3x^2 - 6(2+√5) + 6√5

Mathematics

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,   Mathematics

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:    .

Mathematics

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

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