Question

find the quadratic polynomial if sum of zoroes are 1 by4 and product of zeroes is -1

Answer 1

$\alpha + \beta = \frac{1}{4} \\ \\ \alpha \beta = - 1 \\ \\ polynomial : {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ polynomial : {x}^{2} - \frac{1}{4} \: x - 1 \\ \\ \boxed{polynomial : {x}^{2} - \frac{1}{4} \: x - 1}$

Answer 2

Answer:

$\boxed{\sf{Polynomial\:is\:4x^2-x-4=0}}$

Step-by-step explanation:

Formulas :

Sum of zeroes of quadratic polynomial = - b/a

Product of zeroes of quadratic polynomial = c/a

Let the polynomial be ax² + bx + c = 0

Given sum of zeroes = 1 / 4

So : - b/a = 1 / 4

⇒ - b can be 1

⇒ b can be - 1

⇒ a can be 4

Product of zeroes = - 1

So c / a = - 1

⇒ a is 4 .

⇒ so c can be - 4

Hence our polynomial was :

ax² + bx + c = 0

⇒ 4 x² + ( - 1 ) x - 4 = 0

⇒ 4 x² - x - 4 = 0