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:q(y) = 7y2 – (11/3)y – 2/3
Answer» Given, q(y) = 7y² – (11/3)y – 2/3 We put q(y) = 0 ⇒ 7y² – (11/3)y – 2/3 = 0 ⇒ (21y² – 11y -2)/3 = 0 ⇒ 21y² – 11y – 2 = 0 ⇒ 21y² – 14y + 3y – 2 = 0 ⇒ 7y(3y – 2) – 1(3y + 2) = 0 ⇒ (3y – 2)(7y + 1) = 0 This gives us 2 zeros, for y = 2/3 and y = -1/7 Hence, the zeros of the quadratic equation are 2/3 and -1/7. Now, for verification Sum of zeros = – coefficient of y / coefficient of y² 2/3 + (-1/7) = – (-11/3) / 7 -11/21 = -11/21 Product of roots = constant / coefficient of y² 2/3 x (-1/7) = (-2/3) / 7 – 2/21 = -2/21 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:q(y) = 7y2 – (11/3)y – 2/3

Answer»

Given,

q(y) = 7y² – (11/3)y – 2/3

We put q(y) = 0

⇒ 7y² – (11/3)y – 2/3 = 0

⇒ (21y² – 11y -2)/3 = 0

⇒ 21y² – 11y – 2 = 0

⇒ 21y² – 14y + 3y – 2 = 0

⇒ 7y(3y – 2) – 1(3y + 2) = 0

⇒ (3y – 2)(7y + 1) = 0

This gives us 2 zeros, for

y = 2/3 and y = -1/7

Hence, the zeros of the quadratic equation are 2/3 and -1/7.

Now, for verification

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

2/3 + (-1/7) = – (-11/3) / 7

-11/21 = -11/21

Product of roots = constant / coefficient of y²

2/3 x (-1/7) = (-2/3) / 7

– 2/21 = -2/21

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