Question

(2) Find the quadratic equation whose roots are the reciprocals of the roots
of x^2 + 4x - 10 = 0.
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Answer 1

Explanation:

let a and b be the roots of given equation

a+b=-4

product of roots =ab=-10

we have to find quadratic equation whose roots are 1/a and 1/b(reciprocal)

sum of roots = 1/a+1/b=a+b/ab

==-4/-10=4/10

product of roots=1/a*1/b=1/ab=-1/10

x^2-(sum of roots)x + product of roots=0

x^2-4x/10-1/10=0

10x^2-4x-1=0