Question

The roots of 4{{x}^{2}}+6px+1=0
are equal, then the value of p is [MP PET 2003]
A) \frac{4}{5} B) \frac{1}{3} C) \frac{2}{3} D) \frac{4}{3}

Answer 1

Hi ,

compare 4x² + 6px + 1 = 0 with ax² + bx + c = 0

we get ,

a = 4 ,

b = 6p ,

c = 1 ,

discreaminant = 0

[ since roots are equal ]

b² - 4ac = 0

( 6p )² - 4 × 4 × 1 = 0

( 6p )² = 16

6p = ± √16

6p = ± 4

p = ± 4/6

p = ± 2/3

Therefore ,

p = 2/3 or p = - 2/3

I hope this helps you.

: )

Answer 2

So this is your answer

x=-b±√b²-4ac

2a

x=-6p±√(6p)²-4×4×1

2×4

x=-6p±√36p²-16

8

x=-6p±6p-4

2

x=-6p+6p-4 x=-6p-6p-4

2 2

x=-4 x=-12p-4

2 2

x=-2 x=-12p-2

so put the x=-2

4x²+6px+1=0

4(2)²+6p(2)+1=0

4(4)+12p+1=0

16+12p+1=0

12p=-17

p=-17

12

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