If one root of the equation ^2+ 4+ = 0 is three times the other, then find the value of (3^2/).
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We know that if m and n are the roots of a quadratic equation ax
2+bx+c=0, the sum of the roots is m+n=− ab
and the product of the roots is mn= ac
.
Let m and n be the roots of the given quadratic equation x
2
+px+q=0. It is given that one of the root is three times the other, therefore,m+n=− ab=− 1p=−p
⇒m+n=−p
⇒3n+n=−p
⇒4n=−p
⇒n=− 4p
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