(2p+1)X^2-(7p+2)X+7p-3=0....for what value of p that equation will have two equal root
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(2p+1)x²-(7p+2)x+(7p-3) = 0
a =2p+1, b = 7p+2, c = 7p-3
for roots to be equal discriminant = 0
b²-4ac = 0
b² = 4ac
(7p+2)² = 2(2p+1)(7p-3)
49p²+4+28p = 56p²+4p-12
(56-49)p²+(4-28)p+(-12-4) = 0
7p²-24p-16 = 0
7p²-28p+4p-16 = 0
7p(p-4)+4(p-4) = 0
(7p+4)(p-4) = 0
p = 4 or p = -4/7
a =2p+1, b = 7p+2, c = 7p-3
for roots to be equal discriminant = 0
b²-4ac = 0
b² = 4ac
(7p+2)² = 2(2p+1)(7p-3)
49p²+4+28p = 56p²+4p-12
(56-49)p²+(4-28)p+(-12-4) = 0
7p²-24p-16 = 0
7p²-28p+4p-16 = 0
7p(p-4)+4(p-4) = 0
(7p+4)(p-4) = 0
p = 4 or p = -4/7
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