Question

Find a quadratic polynomial each with the given numbers as the sum and the product of its zeros respectively
1) 1/4,-1

Please help me in the sum by step by step explanation

Answer 1

Answer:

$4 {x}^{2} + x - 1 = 0$

Step-by-step explanation:

$Let, \: \alpha \: and \: \beta \: be \: the \: zeroes \: of \: the \: quadratic \: polynomial$

$Given = sum \: of \: its \: zeroes = \alpha + \beta = \frac{ 1}{4}$

$product \: of \: its \: zeroes = - 1$

We know that,

$x^{2} - ( \alpha + \beta )x + ( \alpha \times \beta )$

${x }^{2} - ( \frac{1}{4})x - 1 = 0$

$\frac{{4x}^{2} + x - 1 }{4} = 0$

$\boxed{ 4 {x}^{2} + x - 1 = 0}$