Question

find a quadratic polynomial whose zeroes are 1/4 and -1 as the sum and product of it's zeroes respectively

Answer 1

sum of zeroes = -b/a

product of zeroes = c/a

1/4=-b/a

b=-1

a=4

c/a=-1

c/4=-1

c=-4

polynomial is 4x^2-x-4

Answer 2

The required polynomial is $4x^2-x-4=0$

Step-by-step explanation:

Given : The zeros are $\frac{1}{4}$ and -1 as the sum and product of it's zeroes respectively.

To find : A quadratic polynomial ?

Solution :

The quadratic polynomial is $x^2-(\text{sum of zeros})x+\text{product of zeros}=0$

The sum of zeros is $\alpha+\beta =\frac{1}{4}$

The product of zeros $\alpha \beta=-1$

The quadratic polynomial is $x^2-(\alpha+\beta)x+\alpha \beta=0$

Substitute the values,

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

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

$4x^2-x-4=0$

Therefore, the required polynomial is $4x^2-x-4=0$

#Learn more

Find the quadratic polynomial whose sum of zeros and product of zeros are respectively to 1 by 4 and 1 by 4 respectively

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