Find the value of p for which the equation (p+3)x²-(5-p)x + 1 =0 will have equal roots.
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Answer:
(p−3)x 2
−2px+5p=0
For roots to be real, D≥0
(−2p)
2
−4(5p)(p−3)≥0
⇒4p
2
−4(5p
2
−15p)≥0
⇒p
2
−5p
2
+15p≥0
⇒−4p
2
+15p≥0
⇒4p
2
−15p≤0
⇒p(4p−15)≤0
⇒0≤b≤15/4
For roots to be +ve, p(0)>0
⇒5p≥0
& vertex should be >0
⇒
2a
−b
>0
⇒
2(p−3)
2p
>0
⇒
p−3
p
>0
⇒p<0 or p>3
⇒p∈(3,15/4).
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