If p and q are distinct prime numbers and if | vedclass

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(C) Let the roots of the quadratic equation $x^2 - px + q = 0$ be $\alpha$ and $\beta$. Since the roots are positive integers,we have $\alpha + \beta

Vedclass · Accepted Answer

$1, 2$

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(C) Let the roots of the quadratic equation $x^2 - px + q = 0$ be $\alpha$ and $\beta$. Since the roots are positive integers,we have $\alpha + \beta = p$ and $\alpha \beta = q$. Since $q$ is a prime number,its only factors are $1$ and $q$. Thus,the roots must be $1$ and $q$. Substituting these into the sum of roots equation: $1 + q = p$. Since $p$ and $q$ are both prime numbers,the only consecutive primes that satisfy $p - q = 1$ are $p = 3$ and $q = 2$. Substituting $p = 3$ and $q = 2$ into the original equation: $x^2 - 3x + 2 = 0$. Factoring the equation: $(x - 1)(x - 2) = 0$. Therefore,the roots are $1$ and $2$.

If $p$ and $q$ are distinct prime numbers and if the equation $x^2 - px + q = 0$ has positive integers as its roots,then the roots of the equation are

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