Question

if alpha and beta are the zeros of the quadratic polynomial P of x = 2 x square - 12 x + 35 find a quadratic polynomial whose zeros are 2 alpha and 2 Beta​

Answer 1

hence alpha and beta are zeroes of the quadratic polynomial p(x)= 2 x square - 12 x + 35
comparing quadratic equation with ax sqare + bx + c
we got that
a = 2
b = -12
c =35

so
the sums of polynomial=alpha + beta = -b/ a
= -(-12)/2
= 12/2
= 6 ..........1


product of zeroes = c/ a
= 35/2 ......2

now we have got a polynomial which zeroes are 2 alpha and 2 Beta​
so the sums of zeroes = -b/a
2 alpha +2 Beta​ = -b/a
2(alpha + beta ) = - b / a

from 1
2(6) = -b/a
12= -b/a ........3

2 alpha × 2 beta = c/a
4 (alpha × beta )= c/a
4(35/2) = c/a
2× 35 = c / a
70 = c/a .........4

comparing 3 and 4
we got that
a=1
b = -12
c = 70
so at last the polynomial is ax sqare -12 x +70

thanks