Given the trinomial 3x2 − 6x + 5, what is the value of the discriminant?

1 answer:

4 0

$\bf \begin{array}{llcccll}
& 3 x^2& -6 x& +5\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\\\\\\
discriminant\implies b^2-4ac\implies (-6)^2-4(3)(5)$

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VashaNatasha [74]

The answer is $3x^4-13x^3-x^2-11x+6$ .

Solution:

Use algebraic identity: $a^m\times a^n=a^{m+n}$

For example: $x^2\times x=x^{2+1}=x^3$

Given expression $(x^2-5x+2)$ and $(3x^2+2x+3)$ .

To multiply these equations.

$(x^2-5x+2)\times(3x^2+2x+3)$

$=x^2(3x^2+2x+3)-5x(3x^2+2x+3)+2(3x^2+2x+3)$

$=(3x^4+2x^3+3x^2)+(-15x^3-10x^2-15x)+(6x^2+4x+6)$

$=3x^4+2x^3+3x^2-15x^3-10x^2-15x+6x^2+4x+6$

Combine like terms together.

$=3x^4+(2x^3-15x^3)+(3x^2-10x^2+6x^2)-15x+4x+6$

$=3x^4-13x^3-x^2-11x+6$

$(x^2-5x+2)\times(3x^2+2x+3)=3x^4-13x^3-x^2-11x+6$

Hence the answer is $3x^4-13x^3-x^2-11x+6$ .

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3 years ago

What is the x-coordinate of the vertex of the parabola whose equation is y = 3x2 + 9x?

Westkost [7]

The vertex is (-1.5, -6.75). So the x-coordinate is -1.5. Hope this helps and if so please leave a good rating and thanks. I really appreciate it. Have a nice day!

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Veseljchak [2.6K]

All you need to do is substitue -2 into the equation for x,

h(-2) = 3(-2) + 1 = -6 + 1 = -5

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timurjin [86]

Answer:

Step-by-step explanation: