If p and q are the roots of the equation x² + px+q=0, then find the values of p and q.
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Answer:
Step-by-step explanation:
It is given that the equation x^2 - px + q = 0 has roots p and q. We can begin solving either by using the sum and product formulae, or by simply substituting the roots into the equation and then work with the resultant equations. Either way, the approach is more or less the same because the Sum and Product of roots formulae are nothing but derivations made by substituting roots into the equation for the standard equation.
Here,
Sum of roots = p
=> p + q = p
=> q = 0
Product of roots = q
=> pq = q
=> pq - q = 0
=> q (p - 1) = 0
=> q = 0, p = 1
The values of p and q hence found are p = 1, and q = 0. This makes the original equation x^2 - x = 0.
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