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The equation x2+3px+p=0, where p is non-zero constant, has equal roots. Find the value of p

Answer :

A quadratic equation has equal roots if and only if the discriminant

[tex]\Delta = b^2-4ac[/tex]

is zero.

So, we have to impose

[tex](3p)^2-4p=0 \iff 9p^2-4p=0 \iff p(9p-4)=0 \iff p=0 \lor\; p=\dfrac{4}{9}[/tex]

Since p is non-zero, the only possible value for p is 4/9.

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