Question

find a quadratic polynomial whose sum of zeros is minus 3 by 2 root 5 and product of zeros is minus 1 by 2 also find the zeros of the polynomial​

Answer 1

Formula: If $p$ be the sum of the zeroes and $q$ be the product of the zeroes of any quadratic polynomial, then it will be represented by

$\quad\quad f(x)=x^{2}-px+q$

Solution:

If $p$ be the sum of the zeroes and $q$ be the product of the zeroes, then

• $p=-\frac{3}{2}\sqrt{5}$
• $q=-\frac{1}{2}$

Therefore the required polynomial is

$\quad f(x)=x^{2}-(-\frac{3}{2}\sqrt{5})x+(-\frac{1}{2})$

$\Rightarrow f(x)=x^{2}+\frac{3}{2}\sqrt{5}x-\frac{1}{2}$

$\Rightarrow f(x)=\frac{1}{2}(2x^{2}+3\sqrt{5}x-1)$

$\Rightarrow \boxed{f(x)=2x^{2}+3\sqrt{5}x-1}$

This is the required polynomial.

Answer 2

Answer:4√5x²-6x-2√5

Step-by-step explanation

We know p(x)= k(x²-Sx-p)

So, here

p(x)= k(x²-3x-1/2)

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2√5

Now take lcm of 2√5 and 2 and forget the k and thr denominator.

We get 4√5x²-6x-2√5