Question

If a and B are the zeros of the polynomial x^2-x-6, find a quadratic polynomial whose zeros are
+2 B) and (2a +3 B).​

Answer 1

Answer:

zeroes of another quadratic polynomial = 2B and 2a +3 B

Step-by-step explanation:

sum of zeroes = 2B + 2a+3B

= 5B +2a

product of zeroes = 2B (2a +3B)

= 4aB + 6B square

$polynomial \: = {x}^{2} + x(sum \: of \: zeroes ) \\ + product \: of \: zeroes \\ \\ polynomial \: = {x}^{2} + (5b + 2a)x + 4ab + {b}^{2}$

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Answer 2

Answer:

${x}^{2} - 12x - 20$

Step-by-step explanation:

$\alpha \: and \: \beta \: are \: zeros \: of \: p(x) = {x}^{2} - x - 6 \\ \\ \alpha = \frac{ - b}{a} = \frac{ - 1}{1} = - 1 \\ \\ \beta = \frac{c}{a} = \frac{ - 6}{1} = - 6$

$if \: another \: polynomial \: has \: zero\\ = 2 \times \beta and \: 2 \alpha + 3 \beta \\ \\the \: zeros \: are \: 2 \times ( \beta ) = 2 \times ( - 6) = - 12 \\\\ 2 \alpha + 3 \beta = 2( - 1) + 3( - 6) \\ = - 2 - 18 = -20$

$polynomial = {x}^{2} - 12x - 20$

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