Question

If alpha and beta are the zeroes of x²-x-2 ,form a quadratic polynomial whose zeroes are. 2 alpha +1, 2beta +1
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Answer 1

P(x) = x^2 - x-2

$\boxed{\textbf{By middle term splitting}}$

0 = x^2 -(2-1) x -2

0= x^2 -2x+x -2

0= x(x-2) +1(x-2)

0= (x+1) (x-2)

x+1 = 0

x=-1

$\alpha = - 1$

x-2 = 0

x= 2

$\beta = 2$

$2 \alpha + 1 = 2 \times - 1 + 1$

$= - 2 + 1$

= -1

$2 \beta + 1 = 2 \times 2 + 1$

$= 4 + 1$

=5


General form of quadratic equation:-

p(x) = x^2 -(alpha+beta)x + alpha × beta

So , the new equation is :-

0= x^2 -(-1+5)x + (-1)×5

0= x^2 -(4)x -5

0=x^2 -4x -5

Answer 2

hope it will help you