Question

if alpha and beta are zero of P of x is equal to 2 x square - 3 x + 1 then find the polynomial whose zeros are alpha + 2 and beta + 2​

Answer 1

$\:\: \underline{\underline{\bf{\large\mathfrak{~~Solution~~}}}}$

$x = x {}^{2} - 3x + 1 \\ = > x {}^{2} - 4x + 1 = 0$

now the ...sum of the zeroes is....

(a+b)=4

and product is ....

ab=1

...........

now

now the equation with zeroes (a+2) and (b+2)..is

$x {}^{2} - (a + 2 + b + 2)x + (a + 2)(b + 2) = 0 \\ = > x {}^{2} - ( 4 + 4)x + (ab + 2(a + b) + 4) = 0 \\ = > x {}^{2} - 8x + (1 + 2(4) + 4) = 0 \\ = > x {}^{2} - 8x + 13 = 0$