Question

find the zeros of each of the following quadratic polynomial and verify the relationship between the zeros and their coefficients- xi)
$p(y)=y^2+(3√5/2)y-5$
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Answer 1

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.Read more on Sarthaks.com - https://www.sarthaks.com/623584/p-y-y-2-35-2-y-5