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Question
If p and q are the roots of the equation x2 – px + q = 0, then ______.
Options
p = 1, q = –2
p = 1, q = 0
p = –2, q = 0
p = –2, q = 1
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Solution
If p and q are the roots of the equation x2 – px + q = 0, then p = 1, q = –2.
Explanation:
Given that p and q be the roots of the equation x2 − px + q = 0
Then find the value of p and q.
Here, a = 1, b = –p and, c = q
p and q be the roots of the given equation
Therefore, sum of the roots
`p + q = (-b)/a`
= `(-p)/1`
= –p
q = –p – p
= –2p ...(i)
Product of the roots
`p xx q = q/1`
As we know that `p = q/q`
= 1
Putting the value pf p = 1 in equation (i)
q = −2 × 1
= –2
Therefore, the value of p = 1; q = –2
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