If the roots of a quadratic equation are 1 ± √5, then what is the product of the roots?
Quadratic equations are those that have the highest degree equal to two. They have many applications in various fields.
Answer: If the roots of a quadratic equation are 1 ± √5, then the product of the roots is -4.
Let's understand in detail.
Explanation:
We are given that the roots of the quadratic equation are 1 ± √5
We can also write that the two roots of the quadratic equation as (1 + √5) and (1 − √5)
Now, if we multiply them, we get the product of the roots.
Hence, (1 + √5) (1 − √5) = 12 − (√5)2 [we used the formula of a2 − b2 = (a − b) (a + b)]
= 1 − 5
= -4