Quadratic Equation

Algebra Level 2

If $p$ and $q$ are prime numbers such that the equation $x^2 - px + q = 0$ has 2 distinct real roots, can we determine the value of $p + q$ ?

Yes, it must be 10 Yes, it must be 18 Yes, it must be 8 No, there are multiple possible values

1 solution

Tina Sobo
Nov 27, 2016

If p and q are the roots of the equation, and the equation is in the form of Ax^2 + Bx + C = 0, then B = sum of roots = -p (from equation) = p + q (roots given) --> p+q = -p --> q = -2p C = product of roots = q (from equation) = pq (roots given) --> q-pq = 0 = q(p-1)=0 --> q = 0 or p=1

If q=0, then subbing into the Bx part - 0 = -2p --> p = 0 and the roots are not distinct Thus, p=1, and q=-2*1 = -2.

p+q = -1; which isn't an option. I'm not sure I'd classify the answer as "not enough information given" - but 8, 10, and 18 certainly aren't the sum of the roots.

Wrong solution. The question mentions the quadratic equation has 2 distinct real roots and not that $p$ and $q$ are roots of the equation

Krutarth Patel - 6 months ago

Quadratic Equation

1 solution

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