Question

Find a quadratic polynomial whose sum and product of zeroes are - 3 / 2 under root 5 and minus 1 divided by 2

Answer 1

Question:

Find a quadratic polynomial whose sum and product of zeros are $\frac{-3}{2\sqrt{5}}$ and $\frac{-1}{2}$.

Answer:

For forming a quadratic polynomial whose zeros are given is very easy by using the following formula:

$\boxed{\bold{\mathsf{k[x^2 + (\alpha + \beta)x + (\alpha \times \beta)]}}}$

Where k is the constant term.

Given that,

$\alpha + \beta = \frac{-3}{2\sqrt{5}}$

$\alpha \times \beta = \frac{-1}{2}$

By substituting the given values,

$\bold{\mathsf{k[x^2 + (\frac{3}{2\sqrt{5}}x) + (\frac{-1}{2})]}}$

Substituting k = 2 (for cancelling 2 from denominator)

$\bold{\mathsf{2[x^2 + (\frac{3}{2\sqrt{5}}x) + (\frac{-1}{2})]}}$

$\bold{\mathsf{x^2 + (\frac{3}{\cancel{2}\sqrt{5}}x) + (\frac{-1}{\cancel{2}})}}$

$\bold{\mathsf{x^2 + (\frac{3}{\sqrt{5}}x) + (-1)}}$

Multiplying $\sqrt{5}$ (for cancelling $\sqrt{5}$ from the denominator)

$\bold{\mathsf{\sqrt{5}x^2 + (\frac{3}{\cancel{\sqrt{5}}}x) + (\sqrt{-5}}})$

$\boxed{\bold{\mathsf{\sqrt{5}x^2 + 3x + \sqrt{-5}}}}$

Therefore, the quadratic polynomial is $\sqrt{5}x^2 + 3x + \sqrt{-5}$.

Answer 2

Step-by-step explanation:

HOPE IT HELPS.

ID YOU NEED EXPLANATION ASK FOR IT IN COMMENTS.

IF IT HELPS MARK MY ANSWER BRAINLIEST