Question

If one root of the quadratic equation 3x?+px+4=0 is 2/3, then find the value
of p and the other root of the equation.
OR
The roots a and B of the quadratic equation XP-5:(-3(k-1)=0 are such that a-
B=1. Find the value k.​

Answer 1

Answer:

$x = \frac{2}{3} \\ 3 {x}^{2} + px+4=0\\3{(\frac{2}{3})}^{2} + p( \frac{2}{3}) + 4 = 0 \\ 3 \times \frac{4}{9} + \frac{2p}{3} + 4 = 0 \\ \frac{4}{3} + \frac{2p}{3} + 4 = 0 \\ \frac{4 + 2p + 12}{3} = 0 \\ 4 + 2p + 12 = 0 \times 3 \\ 4 + 2p + 12 = 0 \\ 16 + 2p = 0\\ 2p = ( - 16) \\ p = \frac{( - 16)}{2} \\ p = ( - 8) \\ 3 {x}^{2} + px + 4 = 0 \\ 3 {x}^{2} + ( - 8)x + 4 = 0 \\ 3 {x}^{2} - 8x + 4 = 0 \\ 3 {x}^{2} - 6x - 2x + 4 = 0 \\ (3 {x}^{2} - 6x) - (2x + 4) = 0 \\ 3x(x - 2) - 2(x - 2) = 0 \\ (x - 2)(3x - 2) = 0 \\ (x - 2 = 0)(3x - 2 = 0) \\ x = 2, \: x = \frac{2}{3}$