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anyanavicka [17]
2 years ago
9

Find a polynomial equation that has roots of -2 and double root 3

Mathematics
1 answer:
lbvjy [14]2 years ago
6 0

Answer:

x³ + 2x² -3x +6

Step-by-step explanation:

We need to find the polynomial whose roots are ,

  • -2 , √3 and √3.

Say of we have zeroes as , α , β and γ , then the polynomial is ,

=> p(x) = k[ (x - α ) ( x - β) ( x - γ) ]

  • where k is constant. Substituting the respective values , we have ,

=> p(x) = k [ ( x - (-2)) ( x - √3) ( x -√3)]

=> p(x) = k[ (x+2)(x² - 3)]

=> p(x) = k[ x(x² - 3) + 2(x² - 3) ]

=> p(x) = k[ x³ - 3x + 2x² - 6 ]

=> p(x) = k[ x³ + 2x² - 3x - 6 ]

<h3><u>Hence </u><u>the</u><u> </u><u>cubic </u><u>polynomial</u><u> is</u><u> </u><u>x³</u><u> </u><u>+</u><u> </u><u>2</u><u>x</u><u>²</u><u> </u><u>-</u><u> </u><u>3x</u><u> </u><u>+</u><u> </u><u>6</u><u> </u><u>.</u></h3>
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