If -1 and 3 are the roots of ×square+p×+q=0, find the values of p and q.
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Answer :
p = -2
q = -3
Given :
◘ Quadratic equation, x² + px + q = 0
◘ -1 and 3 are zeroes of the polynomial.
To find :
◘ Values of p and q
Solution :
- -1 is zero of the polynomial,
Put x = -1,
⇒ x² + px + q = 0
⇒ (-1)² + p(-1) + q = 0
⇒ 1 - p + q = 0
⇒ p - q = 1
----> equation (1)
- 3 is zero of the polynomial,
Put x = 3,
⇒ x² + px + q = 0
⇒ 3² + p(3) + q = 0
⇒ 9 + 3p + q = 0
⇒ 3p + q = -9
----> equation (2)
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From equations (1) and (2),
p - q = 1
3p + q = -9
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4p = -8
p = -8/4
p = -2
Substitute value of p in any equation,
I am substituting in equation (1)
p - q = 1
-2 - q = 1
-q = 1 + 2
-q = 3
q = -3
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HOPE IT HELPS..!
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