Question

Find a quadratic polynomial whose sum of zeros and product of zeros are 1/4, -1 respectively

Answer 1

Answer:

$\mathfrak {\large \green{ \underline{ \underline{answer = {4x}^{2} - x - 4 = 0 }}}}$

Step-by-step explanation:

$\mathfrak {\large \green{ \underline{ \underline{to \: find \: quadratic \: polynomial}}}} \\ \mathfrak {\large \green{ \underline{ \underline{sum \: of \: zeroes = \frac{1}{4} }}}} \\ \\ \mathfrak {\large \green{ \underline{ \underline{product \: of \: zeroes = - 1}}}} \\ \\ \mathfrak {\large \red{ \underline{ \underline{formula \: of \: quadratic \: polynomial}}}} \\ \mathfrak {\large \blue{ \underline{ \underline{ {x}^{2} - ( \alpha + \beta )x + \alpha \beta }}}} \\ \large \blue{ {x}^{2} - ( \frac{1}{4})x + ( - 1 ) = 0 } \\ \large \blue{ \frac{4 {x}^{2} - x - 4 }{4} = 0 } \\ \large \green{ {</em><em>4</em><em>x}^{2} - x - 4 = 0 }$

Answer 2

QUESTION:

Find a quadratic polynomial whose sum of zeros and product of zeros are 1/4, -1 respectively

CONCEPT USED :

We know that quadratic equation is in the form of

$\huge\orange {a {x}^{2} + bx + c = 0}$

where;

b = sum of zeroes

c = product of zeroes

In other form we can write this equation;

$\red { {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes)}$

now come to main question;

GIVEN :

Sum of zeroes = 1/4

product of zeroes = -1

Using the formula and putting the value in the equation;

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

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

FINAL ANSWER :

$\huge\blue {4 {x}^{2} - x + 4 = 0}$