Question

If a,b are zeroes of quadratic polynomial x^2-3x+2, find a quadratic polynomial whose zeroes are 1/2a+b, 1/2b+a.
Please answer quickly. Thank you:)

Answer 1

Answer:

✅Here's your answer

${x}^{2} - 3x + 2 \\ \\ {x}^{2} - 2x - x + 2 \\ \\ x(x - 2) - 1(x - 2) \\ \\ (x - 2)(x - 1) \\ \\ x = 1 \: and \: 2$

✔Here's a is 1 and b is 2...

So

$\alpha = \frac{1}{2a + b} = \frac{1}{4} \\ \\ \beta = \frac{1}{2b + a} = \frac{1}{5}$

$\alpha \beta = \frac{1}{20} \\ \\ \alpha + \beta = \frac{9}{20}$

$k( {x}^{2} - ( \frac{9}{20} )x + \frac{1}{(20} )) = 0 \\ \\ k( \frac{ {20x}^{2} - 9x + 1}{20} ) = 0 \\ \\ let \: k \: be \: 20 \\ \\ \\ 20 {x}^{2} - 9x + 1 = 0$

$so \: the \: polynomial \: is \\ \\ 20 {x}^{2} - 9x + 1$

Hope it helps✌

✅quadratic polynomial

= k(x^2-(sum of zeroes) +(product of zeros)