Question

In 6.
The sum of the roots of a quadratic equation is 7 and the sum of their
cubes is 133. To find the quadratic equation, fill in the empty boxes.
Solution : Suppose, a and B are the roots of the quadratic equation in
variable x.
​

Answer 1

Answer:

a+b=7

a^3+b^3=133

(a+b) (a^2+b^2+ab) =133

(a+b) (a^2+b^2+2ab-ab) =133

7*((a+b) ^2-ab) =133

7*(49-ab) =133

49*7-7ab=133

343-7ab=133

-7ab=133-343

-7ab=-210

ab=210/7

ab=30

quadratic equation,

x^2-(a+b) x+ab=0

x^2-7x+30=0.