An algebra problem by Anoopam Mishra
Algebra
Level
2
The roots of the quadratic equation x^2 - 30x + b = 0 are positive and one of them is square of the other. If the roots are r and s with r>s then the value of b + r - s is
The answer is 145.
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1 solution
Let the roots be a and a^2.
Then a + a^2 = 30 (sum of roots = -b/a)
Solving the equation we get 5 and -6, we reject -6 because the roots are positive.
We get r=25 and s=5 (r>s) a*a^2 = b = 5^3 = 125 (product of roots = c/a)
b+r-s = 125+25-5 = 145