Question

Find a quadratic polynomial the sum and product of whose zeros are 1 by 4 and -1 by 8 respectively

Answer 1

Answer:

If the zeroes are α and β,

$\alpha + \beta = \frac{1}{4} \\\alpha \beta = \frac{-1}{8}$

A quadratic polynomial can be written as -

$k[x^{2} + (\alpha + \beta)x + \alpha \beta]$

Substituting values,

$k[x^{2} + \frac{x}{4} - \frac{1}{8}]$

Taking LCM as 8,

$k_{1} [8x^{2} + 2x - 1]$

This is the required polynomial.

Answer 2

Step-by-step explanation:

$let \: sum \: of \: the \: roots \: \\ \alpha + \beta = 1 \div 4 \\ and \: \alpha \beta = - 1 \div 9 \\ then \\ polynomial = {x }^{2} - ( \alpha + \beta )x + \alpha \beta = 0\\ {x}^{2} + (- 1 \div 4 )+ ( - 1 \div 9) = 0 \\ {x}^{2} - 1 \div 4x - 1 \div 9 = 0 \\ 36 {x}^{2} - 9x - 4 = 0$