Question

Frame the question 1-3√5 and 1+3√5

Answer 1

Answer:

Given: Two roots of the quadratic equation are 1-3√5 & 1+3√5.

To find: Frame the equation.

Step-by-step explanation:

Let α= 1-3√5 & β= 1+3√5.

Therefore, Sum of the roots: α+β = 1-3√5 + 1+3√5.

α+β = 1+1. α+β = 2.

Product of roots: αβ = (1-3√5)(1+3√5)

=>αβ = 1+3√5 -3√5 - 9×5.

αβ = 1 -45.

αβ = -44.

Now,

The quadratic equation is, x² -(α+β)x +αβ= 0

∴ x² -2x + (-44)= 0

→ x² -2x - 44= 0

Answer 2

Answer:

2 roots of the equation are 1-3 root 5 and 1+3 root 5

let,

alpha=1-3 root 5

beta=1+3 root 5

sum of roots=alpha+beta

=1-3 root 5+1+3 root 5

=2

product of roots = alpha.beta

= (1-3 root 5)(1+3 root 5)

= 1^2 - (3 root 5)^2

= 1 - 9(5)

= 1 - 45

= - 44

GENERAL FORM OF QUADRATRIC EQUATION: