Question

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

Answer 1

Using formula :-

Sum of zeros = α + β

Product of zeros = α β

So,

Sum of zeros = α + β = $\frac{1}{4}$

Product of zeros = α β = -1

Now, If α and β are zeros of any quadratic polynomial, then the quadratic polynomial equation can be written directly as:

x² – (α + β)x + αβ = 0

x² – $\frac{1}{4}$ x + (-1) = 0

4x² – x – 4 = 0

Hence, 4x² – x – 4 is the quadratic polynomial.