If the roots of a quadratic equation are 1±√5, then the product of the roots is:

Solution:

A quadratic equation is an algebraic expression of the second degree in x.

The standard form of a quadratic equation is ax2 + bx + c = 0,

where a, b are the coefficients,

x is the variable, and

c is the constant term.

The roots of a quadratic equation given is 1 ± √5

It can be written as

(1 + √5) and (1 - √5)

By multiplication, we can obtain the product of the roots

(1 + √5)(1 - √5)

Using the algebraic identity a² - b² = (a + b)(a - b)

= 1 - √5²

= 1 - 5

= -4

Therefore, the product of the roots is -4.

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If the roots of a quadratic equation are 1±√5, then the product of the roots is:

Summary:

If the roots of a quadratic equation are 1±√5, then the product of the roots is -4.