Question

If one root of the quadratic equation 3x2+px+4=0 is 2/3, then find the value
of p and the other root of the equation.

Answer 1

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Solution:-

As 2/3 is one root of the equation, let us apply it in the x:

3x^2+px+4=0

3(2/3)^2+(2/3)p+4=0

3(4/9)+(2/3)p+4=0

4/3+2p/3+4=0

16/3+2p/3=0

2p/3= -16/3

p= -16/3 \times× 3/2

p = -8

3x^2+px+4=0

Substitute p = -8

3x^2 - 8x + 4 = 0

3x^2 - 6x - 2x + 4 = 0

3x(x-2) -2(x-2)

(3x-2)=0 and x-2=0

3x = 2 and x = 2

x = 2/3 or x = 2

Hence, the other root of the quadratic equation is: x = 2