Question

If alpha and beta are the zeroes of the quadratic polynomial
f(x) = x^2+x-2

then find a polynomial whose zeroes
are
2(alpha) +1 and
2(beta) +1.​

Answer 1

Step-by-step explanation:

$f(x) = {x}^{2} + x - 2 \: and \: \alpha\: and \: \\ \beta \: are \: roots \: \\ then \\ {x}^{2} + x - 2 = {x}^{2} + 2x - x \: + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 2 \\ = (x + 2)(x - 1) = 0 \\ x = - 2 \: and \: 1$

the polynomial whose roots are

$2 \alpha + 1 \: and \: 2 \beta + 1$

then polynomial would be

$(x - (2 \alpha + 1))(x - (2 \beta + 1))$

putting the value of

$\alpha \: and \: \beta$

further you should as you can do it the similar queation further