Question

Find the values of the coefficients b and c in the quadratic equation 3x2+bx+c if the sum and product of the roots of this equation are respectively 7/3 and 13/3.

Answer 1

b = -7

c = 13

Explanation:

`3x^2+bx+c`

`\textsf{sum of roots}=(-b)/(a)\\\\\textsf{product of roots}=(c)/(a)`

`\textsf{Given sum of roots}=\frac73:`

`\implies (-b)/(a)=\frac73`

`\implies a=3, b=-7`

`\textsf{Given product of roots}=(13)/(3):`

`\implies (c)/(a)=(13)/(3)`

`\implies a=3, c=13`

Therefore,

`3x^2-7x+13`

NB: The actual calculated roots are imaginary numbers as the function
`f(x)=3x^2-7x+13` does not intercept the x-axis

Answer 2

a = 3

b = -7

c = 13

Explanation:

`\sf{given \ equation: 3x^2+bx+c`

`\sf{sum \ of \ roots :\sf(7)/(3)`

`\sf{product \ of \ the \ roots:(13)/(3)`

• a = 3
• b = b
• c = c

`\sf{sum \ of \ roots \ = -(coefficient \of \ x)/(coefficient \ of \ x^2) }`

`\sf (-b)/(3) = (7)/(3)`

`\sf b = (-7*3)/(3)`

`\sf b =- 7`

`\sf{product \ of \ roots \ = (constant \ term)/(coefficient \ of \ x^2) }`

`\sf{(c)/(3) =(13)/(3)`

`\sf c = (13*3)/(3)`

`\sf c = 13`

Therefore found that a = 3, b = -7, c = 13