Question

If alpha and beta are the zeros of the quadratic polynomial x^2-x-2. Find another quadratic polynomial whose zeros are 2alpha+1 and 2beta+1.

Answer 1

Nice question mate!!!✌✌✌

Answer is x^2 - 4x - 5

Refer attachment for understanding the process step by step...

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Answer 2

According to given sum,

$= > \: {x}^{2} - x - 2 = 0$

$= > \: {x}^{2} - 2x + x - 2 = 0$

$= > \: x(x - 2) + 1(x - 2) = 0$

$= > \: (x - 2)(x + 1) = 0$

$so \: \alpha = 2 \: \:and \: \beta = - 1$

From the given question,


$2 \alpha + 1 = 2(2) + 1 = 5 \\ 2 \beta + 1 = 2( - 1) + 1 = - 1$
sum of zeroes= 5+(-1)=4

product of zeroes = 5 (-1)= -5

Quadratic polynomial is in the form,

${x}^{2} - (p + q) + pq$
where p & q are zeroes.

$= > \: {x}^{2} - 4x - 5$


:-)Hope it helps u.