Mathematics: Could someone do all the problems and/or check my work?

23,598 because 513 x 40 = ( 500 x 40 ) + ( 10 X 40 ) + ( 3 x 40 ) = 20 000 + 400 + 120 = 20,520 and another partial product is 513 x 6 = ( 500 x 6 ) + ( 10 x 6 ) + ( 3 x 6 ) = 3 000 + 60 + 18 = 3,078. so 20,520 + 3,078 = 23,598...

Could someone do all the problems and/or check

Ответ:

klrm8045

10.03.2022

Mathematics

NOTES: To find the intercepts/roots:

move everything to one side and 0 on the otherfactor the equationapply the Zero Product Property (set each factor equal to 0)solve for x

11. x = {-4, 0, 5}

Step-by-step explanation:

$x^3=x^2+20x\\x^3-x^2-20x=0\\x(x^2-x-20)=0\\x(x-5)(x+4)=0\\x=0\quad x-5=0\quad x+4=0\\x=0\quad x=5\quad x=-4\\Solutions:\ x=\{-4, 0, 5\}$

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12. x = No real solution

Step-by-step explanation:

$x^4+13x^2+40=0\\(x^2+5)(x^2+8)=0\\x^2+5=0\quad \qquad x^2+8=0\\x^2=-5\qquad \qquad x^2=-8\\x=\pm \sqrt{-5}\quad \quad x=\pm \sqrt{-8}\\ \text{Neither solution is a real number}$

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13. x = {-2, 2}

Step-by-step explanation:

$x^4-x^2=x^2+8\\x^4-2x^2-8=0\\(x^2-4)(x^2+2)=0\\x^2-4=0\quad \qquad x^2+2=0\\x^2=4\qquad \qquad x^2=-2\\x=\pm \sqrt{4}\quad \quad x=\pm \sqrt{-2}\\x=\pm 2\qquad \text{x is not a real solution}\\Solutions: x = \{-2, 2\}$

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14. $\bold{x=\bigg\{-1, 1, -\dfrac{\sqrt{15}}{3}, \dfrac{\sqrt{15}}{3}\bigg\}}$

Step-by-step explanation:

$3x^4-8x^2+5=0\\3x^4-3x^2-5x^2+5=0\\3x^2(x^2-1)-5(x^2-1)=0\\(3x^2-5)(x^2-1)=0\\3x^2-5=0\qquad x^2-1=0\\x^2=\dfrac{5}{3}\qquad \qquad x^2=1\\\\x=\pm \sqrt{\dfrac{5}{3}}\quad \quad x=\pm \sqrt{1}\\\\x=\pm \dfrac{\sqrt{15}}{3}\qquad x=\pm1\\\\Solutions: x = \bigg\{-1, 1, -\dfrac{\sqrt{15}}{3}, \dfrac{\sqrt{15}}{3}}\bigg\}$

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15. $\bold{x=\bigg\{-2, 2, -\dfrac{5}{4}\bigg\}}$

Step-by-step explanation:

$4x^3+5x^2-16x-20=0\\3x^4-3x^2-5x^2+5=0\\x^2(4x+5)-4(4x+5)=0\\(x^2-4)(4x+5)=0\\x^2-4=0\qquad 4x+5=0\\x^2=4\qquad \qquad 4x=-5\\\\x=\pm \sqrt{4}\quad \quad x=\dfrac{-5}{4}\\\\x=\pm 2\qquad \quad x=-\dfrac{5}{4}\\\\ Solutions: x = \bigg\{-2, 2, -\dfrac{5}{4}}\bigg\}$

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