Question 886881
1.) Find a quadratic equation in terms of x whose roots are
a.) 7 and -2

sum of roots = 5
product of roots = -14

the quadratic equation will be

x^2-(sum of roots)x+product of roots=0
x^2-5x-14=0
similarly for all others
b.) 1/2 and 1/3
c.) {{{ 3 +- 4sqrt(5) }}}


3.) Find the value of p so that the roots of 4x^2 = 40x-p difference by 3?

4x^2-40x+p=0

let the roots be  {{{alpha}}} & {{{beta}}}

{{{alpha}}} + {{{beta}}}=-b/a = -(-40/4)=10

{{{alpha}}} * {{{beta}}}= c/a = p/4

{{{alpha}}} - {{{beta}}}=3

({{{alpha}}} - {{{beta}}})^2=9

=({{{alpha}}} + {{{beta}}})^2 -4*{{{alpha}}} * {{{beta}}}=9

substitute
10^2-4*p/4 = 9

100-p=9

p=100-9
p=91