Question

One of the roots of a quadratic equations is 4-√7 find the equation

Answer 1

let one root be alpha=
$4 + \sqrt{7}$
and other root is given beta =
$4 - \sqrt{7}$
therefore alpha × beta
$(4 + \sqrt{7} ) (4 - \sqrt{7} )$
which is equal to c/a
therefore 4square - root(7) square = 16 - 7 = 9
9 = 9/1 = c/a
therefore a = 1
c = 9 .....v1

now we add the roots
alpha + beta =
$4 + \sqrt{7 } + 4 - \sqrt{7}$
= 8 = -b/a
therefore 8/1 = -b/a
a = 1
b = -8 .....VW

from v1 and v2
a=1
b= -8
c= 9
put in equation ax2 +bx + c
to get
x2 - 8x +9