Q. 275.0( 2 Votes )

Find the value of

Answer :

Given quadratic equation, (2p + 1) x2 - (7p + 2) x + (7p – 3) = 0


Comparing the given equation with ax2 + bx + c = 0, we get


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


We know that a quadratic equation ax2 + bx + c = 0 has equal roots (i.e., coincident roots), if b2 – 4ac = 0.


(-(7p + 2))2 – 4(2p + 1) (7p - 3) = 0


49p2 + 28p + 4 – 56p2 + 24p – 28p + 12 = 0


-7p2 + 24p + 16 = 0


7p2 - 24p - 16 = 0


By factorization method,


7p2 – 28p + 4p – 16 = 0


7p (p – 4) + 4(p – 4) = 0


(p – 4) (7p + 4) = 0


(p - 4) = 0 (or) (7p + 4) = 0


p = 4 (or) p = -4/7


For equal roots, roots =


Roots =


Case 1: When p = 4


Roots = (7(4) + 2)/2(2(4) + 1)


= 30/18


= 5/3, 5/3


Case 2: When p = -4/7


Roots = (7(-4/7) + 2)/2(2(-4/7) + 1)


= -2/(-2/7)


= 7, 7


The value of p is 4 or -4/7. The roots are 5/3, 5/3 or 7, 7.


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