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:p(y) = y2 + (3√5/2)y – 5
Answer» Given, p(y) = y² + (3√5/2)y – 5 We put f(v) = 0 ⇒ y² + (3√5/2)y – 5 = 0 ⇒ y² – √5/2 y + 2√5y – 5 = 0 ⇒ y(y – √5/2) + 2√5 (y – √5/2) = 0 ⇒ (y + 2√5)(y – √5/2) = 0 This gives us 2 zeros, for y = √5/2 and y = -2√5 Hence, the zeros of the quadratic equation are √5/2 and -2√5. Now, for verification Sum of zeros = – coefficient of y / coefficient of y² √5/2 + (-2√5) = – (3√5/2) / 1 -3√5/2 = -3√5/2 Product of roots = constant / coefficient of y² √5/2 x (-2√5) = (-5) / 1 – (√5)² = -5 -5 = -5 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:p(y) = y2 + (3√5/2)y – 5

Answer»

Given,

p(y) = y² + (3√5/2)y – 5

We put f(v) = 0

⇒ y² + (3√5/2)y – 5 = 0

⇒ y² – √5/2 y + 2√5y – 5 = 0

⇒ y(y – √5/2) + 2√5 (y – √5/2) = 0

⇒ (y + 2√5)(y – √5/2) = 0

This gives us 2 zeros, for

y = √5/2 and y = -2√5

Hence, the zeros of the quadratic equation are √5/2 and -2√5.

Now, for verification

Sum of zeros = – coefficient of y / coefficient of y²

√5/2 + (-2√5) = – (3√5/2) / 1

-3√5/2 = -3√5/2

Product of roots = constant / coefficient of y²

√5/2 x (-2√5) = (-5) / 1

– (√5)² = -5

-5 = -5

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