Question

A quadratic polynomial has one of its zeros 1 + √5 and it satisfies p(1) = 2. Find the quadratic polynomial.

Answer 1

I think this is wrong qus

Answer 2

Answer:

$p(x)=-\frac{2}{5}(x^2-2x-4)$

Step-by-step explanation:

We have been given the zero  1 + √5.

We know that irrational roots always occurs in pairs. Hence,  1 - √5 is the second zero.

Hence, the quadratic polynomial is

$p(x) =a(x-1-\sqrt5)(x-1+\sqrt5)\\p(x)=a(x^2-2x-4)$

Now, given that p(1)=2

$2=a(1^2-2(1)-4)\\2=-5a\\\\a=-\frac{2}{5}$

Hence, the quadratic polynomial is

$p(x)=-\frac{2}{5}(x^2-2x-4)$