Question

write a quadratic polynomial whose one zero is 3-root5 and product of zeroes is 4

Answer 1

ihope this helps to you

Answer 2

Answer:  The answer is $x^2-6x+4=0.$

Step-by-step explanation:  We are given to write a quadratic equation with one zero  (3 - √5) and product of zeroes 4.

We know that if 'a' and 'b' are two roots of a quadratic equation, then it can be written as

$(x-a)(x-b)=0.$

One root of the quadratic equation is given to be (3 - √5), which is irrational.

We know that the irrational roots of a quadratic equation always occur in pairs, so the other root will be (3 + √5).

Also, the product is

$(3-\sqrt 5)(3+\sqrt 5)=9-5=4,$ which satisfies the given condition.

Therefore, the quadratic equation is

$\{x-(3-\sqrt 5)\}\{x-(3+\sqrt 5)\}=0\\\\\Rightarrow \{(x-3)+\sqrt 5\}\{(x-3)-\sqrt 5\}=0\\\\\Rightarrow (x-3)^2-5=0\\\\\Rightarrow x^2-6x+9-5=0\\\\\Rightarrow x^2-6x+4=0.$

Thus, the required quadratic equation is $x^2-6x+4=0.$