Find a quadratic polynomial whose sum and product respectively of the zeroes are as given .Also find the zeroes of these polynomials by factorization ((-3)/(2sqrt5)), (-1/2)

Question

Find a quadratic polynomial whose sum and product respectively of the zeroes are as given .Also find the zeroes of these polynomials by factorization

(\frac{- 3}{2 \sqrt{5}}), (- \frac{1}{2})

Answer 1

Step 1
Given:

(\frac{- 3}{2 \sqrt{5}}), (- \frac{1}{2})

Sum of the zeroes

= - \frac{3}{2} \sqrt{5} x

Product of the zeroes

= - \frac{1}{2}

Step 2 Finding the zeroes

p (x) = x^{2}

-(sum of the zeroes)+(product of the zeroes)

p (x) = x^{2} - \frac{3}{2} \sqrt{5} x - \frac{1}{2}

p (x) = 2 \sqrt{5} x^{2} - 3 x - \sqrt{5}

2 \sqrt{5} x^{2} - 3 x - \sqrt{5} = 0

2 \sqrt{5} x^{2} - (5 x - 2 x) - \sqrt{5} = 0

2 \sqrt{5} x^{2} - 5 x + 2 x - \sqrt{5} = 0

\sqrt{5} x (2 x - \sqrt{5}) - (2 x - \sqrt{5}) = 0

(2 x - \sqrt{5}) (\sqrt{5} x - 1) = 0

2 x - \sqrt{5} = 0, \sqrt{5} x - 1 = 0

2 x = \sqrt{5}, \sqrt{5} x = 1

x = \frac{\sqrt{5}}{2}, x = \frac{1}{\sqrt{5}}

∴ x = \frac{\sqrt{5}}{2}, \frac{1}{\sqrt{5}}

Expert Answer