2 years ago

X=4y,2x+y=18 solve by substitution show all work

1 answer:

7 0

Here is the math, did it on paper, sorry it’s blue. just add parenthesis around the x in the second equation and add what x equals. then solve as PEMDAS.

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Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots StartRoo

anastassius [24]

Answer:

$a) f(x)=3x^{3}-6x^{2}-15x+30$

Step-by-step explanation:

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

$x_{1}=\sqrt{5}\:x_{2}=2$

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

If one root is in this form $x'=\sqrt{a}+b$ then its conjugate $x''=\sqrt{a}-b$ . is also a root of this polynomial.

Therefore

$x_3=-\sqrt{5}$

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:

$f(x)=3(x-\sqrt{5})(x+\sqrt{5})(x-2)\Rightarrow 3x^{3}-6x^{2}-15x+30$