Question

Find the value of 'P' so that the quadratic equation x 2 -2P(3x-7)-2x+21=0 has equal roots. Please answer fast.. I have my pre-board tomorrow..

Answer 1

x²-2P(3x-7)-2x+21=0
or, x²-6Px+14P-2x+21=0
or, x²-(6P+2)x+(14P+21)=0 ----------------(1)
Let α,β are the roots of the equation (1). Then from the relations between roots and coefficients we have,
α+β=-{-(6p+2)}/1=6P+2 and
α×β=(14P+21)/1=14P+21
Now, it is given that (1) has two equal roots i.e., α=β
∴, β+β=6P+2
or, 2β=6P+2
or, β=3P+1 and
β×β=14P+21
or, β²=14P+21
or, (3P+1)²=14P+21
or, 9P²+6P+1=14P+21
or, 9P²-8P-20=0
or, 9P²-18P+10P-20=0
or, 9P(P-2)+10(P-2)=0
or, (P-2)(9P+10)=0
either, P-2=0
or, P=2
or, 9P+10=0
or, P=-10/9
∴, P=2, -10/9 Ans.

Answer 2

Answer:

Step-by-step explanation:

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