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# Find the values of p for which the quadratic equation:(2p + 1)x2 – (7p + 2)x + (7p – 3) = 0 have equal roots.

(2p + 1)x2 – (7p + 2)x + (7p – 3) = 0

Let us find Discriminant of the given equation. For equal roots of a quadratic equation, Discriminant equals to zero.

Discriminant, D = b2 – 4 ac

Where, a = (2 p + 1), b = (7 p + 2) and c = (7 p – 3)

Putting these values for finding discriminant.

D = (7 p + 2)2 – 4 (2 p + 1) ( 7 p – 3)

D = 49 p2 + 28 p + 4 – (56 p2 + 4 p – 12)

Now for equal roots D = 0

49 p2 + 28 p + 4 – (56 p2 + 4 p – 12) = 0

–7 p2 + 24 p + 16 = 0

7 p2 – 24 p – 16 = 0

For finding values of “p”, apply the Quadratic formula,

We know that the solution of equation ax2 + bx + c = 0 is given by:

For our quadratic equation, a = 7, b = – 24 and c = – 16

So, p = –56/14 or p = 8/14

Thus the possible values of p are – 4 and 4/7

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