Question

Is there anyone capable to answer 'this' quetion? Find the valie of p,if equations 3x²-2x+p=0and 6x²-17x+12=0 have a common root

Answer 1

6x²-17x+12=0

x = 4/3 and 3/2

If common root is 4/3,
3(4/3)² - 2(4/3) + p = 0
⇒ 16/3 - 8/3 + p = 0
⇒ p = -8/3


If common root is 3/2,
3(3/2)² - 2(3/2) + p = 0
⇒ 27/4 - 3 + p = 0
⇒ p = -15/4

Value of p can be -8/3 and -15/4


Hope it helps!

Answer 2

3x² - 2x + P = 0and 6x² - 17x + 12 = 0 has single root common .

now ,

6x² -17x + 12 = 0
6x² - 9x -8x + 12 = 0
3x( 2x -3) -4(2x -3) = 0
(3x -4)( 2x -3) = 0
x = 4/3 , 3/2

hence, may be 4/3 is common root or 3/2 is common , hence , P have two value possibe.

when, 4/3 is a common root , then ,
3(4/3)² -2(4/3) + P = 0
3 × 16/9 -8/3 + P =0
16/3 - 8/3 + P = 0
P = -8/3

again,
when, 3/2 is common root of both equation , then,
3(3/2)² -2(3/2) + P =0
27/4 -3 + P = 0
15/4 + P = 0
P = -15/4

hence, value of P = -8/3 and -15/4