Find the zeros of quadratic polynomials and verify the relationship be

1.	Find the zeros of quadratic polynomials and verify the relationship between the zeros and their coefficients:f(x) = x2 – (√3 + 1)x + √3
Answer» Given, f(x) = x² – (√3 + 1)x + √3 We put f(x) = 0 ⇒ x² – (√3 + 1)x + √3 = 0 ⇒ x² – √3x – x + √3 = 0 ⇒ x(x – √3) – 1 (x – √3) = 0 ⇒ (x – √3)(x – 1) = 0 This gives us 2 zeros, for x = √3 and x = 1 Hence, the zeros of the quadratic equation are √3 and 1. Now, for verification Sum of zeros = – coefficient of x / coefficient of x² √3 + 1 = – (-(√3 +1)) / 1 √3 + 1 = √3 +1 Product of roots = constant / coefficient of x² 1 x √3 = √3 / 1 √3 = √3 Therefore, the relationship between zeros and their coefficients is verified.

Find the zeros of quadratic polynomials and verify the relationship between the zeros and their coefficients:f(x) = x2 – (√3 + 1)x + √3

Answer»

Given,

f(x) = x² – (√3 + 1)x + √3

We put f(x) = 0

⇒ x² – (√3 + 1)x + √3 = 0

⇒ x² – √3x – x + √3 = 0

⇒ x(x – √3) – 1 (x – √3) = 0

⇒ (x – √3)(x – 1) = 0

This gives us 2 zeros, for

x = √3 and x = 1

Hence, the zeros of the quadratic equation are √3 and 1.

Now, for verification

Sum of zeros = – coefficient of x / coefficient of x²

√3 + 1 = – (-(√3 +1)) / 1

√3 + 1 = √3 +1

Product of roots = constant / coefficient of x²

1 x √3 = √3 / 1

√3 = √3

Therefore, the relationship between zeros and their coefficients is verified.