Question

Write the family of quadratic polynomials having - 1/4 and 1 as its zeros.

Answer 1

Plug the value in formula we get                                    x2 –(-1/4)x  + 1/4  = 0multiply by 4 we get                                    4x2   +  x + 1  = 0

Answer 2

Answer: The answer is $4x^2-3x-1.$

Step-by-step explanation:  We are given to write the family of polynomials having zeroes $-\dfrac{1}{4}]$ and 1.

We know that if a polynomial p(x) has zeroes 'a' and 'b', then it can be written as

$p(x)=(x-a)(x-b).$

Since the zeroes of the given polynomial are $-\dfrac{1}{4}]$ and 1., so it can be written as

$q(x)=(x+\dfrac{1}{4})(x-1)\\\\\Rightarrow q(x)=\dfrac{(4x+1)(x-1)}{4}\\\\\Rightarrow 4q(x)=(4x+1)(x-1)\\\\\Rightarrow Q(x)=4x^2-4x+x-1\\\\\Rightarrow Q(x)=4x^2-3x-1.$

Thus, the answer is  $4x^2-3x-1.$