Question

find the zeros of quadratic polynomial 7y^2_11/3y_2/3 and verify the relationship between the zeros and the confficient​

Answer 1

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.

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