Question

find the zeroes of 3x square--x--4 and verify the relationship between the zeroes and coefficient

Answer 1

Hii friend,

P(X) = 3X²-X-4

=> 3X²-4X+3X-4

=> X(3X-4) +1(3X-4)

=> (3X-4) (X+1)

=> (3X-4) = 0 OR (X+1) = 0

=> X = 4/3 OR X = -1

Let Alpha = 4/3 and beta = -1


Relationship between the zeros and the coefficient.


Sum of zeros = (Alpha + Beta) = (4/3+(-1) = 4/3 -1 = 4 -3/3 = 1/3 =Coefficient of X/Coefficient of X²


Product of zeros = (Alpha × Beta) = (4/3 × -1) = -4/3 = Constant term/Coefficient of X².



HOPE IT WILL HELP YOU..... :-)

Answer 2

${3x}^{2} - x - 4 = 0 \\ \\ 3 {x}^{2} - 4x + 3x - 4 \\ x(3x - 4) + 1(3x - 4) \\( x + 1)(3x - 4) \\ x = - 1 \\ x = \frac{4}{3} \\ \\ \\ \alpha + \beta = - \frac{b}{a} \\ \frac{4}{3} - 1 = \frac{1}{3} \\ \ \\ \alpha \beta = \frac{c}{a} \\ \\ \frac{4}{3} \times ( - 1) = \frac{ - 4}{3}$