1951 AHSME Problems/Problem 47
Contents
Problem
If and are the roots of the equation , the value of is:
Solution-1
and can be found in terms of , , and by using the quadratic formula; the roots are
By Vieta's Formula, and . Now let's algebraically manipulate what we want to find:
Plugging in the values for and gives
Solution-2
here and are the roots of the equation ,
now we can convert this equation with roots and .
let, then above equation becomes
square on both sides we get
Again we can change this equation with roots and .
let then, then
then the sum of roots of the above equation is
hence,
See Also
1951 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 46 |
Followed by Problem 48 | |
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