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(v) = v2 + 4√3v – 15
Answer» Given, f(v) = v² + 4√3v – 15 We put f(v) = 0 ⇒ v² + 4√3v – 15 = 0 ⇒ v² + 5√3v – √3v – 15 = 0 ⇒ v(v + 5√3) – √3 (v + 5√3) = 0 ⇒ (v – √3)(v + 5√3) = 0 This gives us 2 zeros, for v = √3 and v = -5√3 Hence, the zeros of the quadratic equation are √3 and -5√3. Now, for verification Sum of zeros = – coefficient of v / coefficient of v² √3 + (-5√3) = – (4√3) / 1 -4√3 = -4√3 Product of roots = constant / coefficient of v² √3 x (-5√3) = (-15) / 1 -5 x 3 = -15 -15 = -15 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(v) = v2 + 4√3v – 15

Answer»

Given,

f(v) = v² + 4√3v – 15

We put f(v) = 0

⇒ v² + 4√3v – 15 = 0

⇒ v² + 5√3v – √3v – 15 = 0

⇒ v(v + 5√3) – √3 (v + 5√3) = 0

⇒ (v – √3)(v + 5√3) = 0

This gives us 2 zeros, for

v = √3 and v = -5√3

Hence, the zeros of the quadratic equation are √3 and -5√3.

Now, for verification

Sum of zeros = – coefficient of v / coefficient of v²

√3 + (-5√3) = – (4√3) / 1

-4√3 = -4√3

Product of roots = constant / coefficient of v²

√3 x (-5√3) = (-15) / 1

-5 x 3 = -15

-15 = -15

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