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| Find the zeroes of the quadratic of the polynomials given below. Find the sum and product the zeroes and verifyrelationship to the coefficients of terms in the given polynomial. |
in general suppose a and b and are the zeroes of the quadratic polynomial p(x)=ax²+bx+c,
where a#0, then (x-a) and (x-B) are the factors of p(x).
Therefore, ax+x+-k(x-a) (x-B), where k & is a constant
=k[x²-(a+b)×+ab]
=kx²-k(a+b)×+kab
Comparing the coefficients of x, a and constant terms on both the sides, we get
a=k,b= -k(a+B) and c=kaß
This gives a+B=-b/a,
| a and B are Greek letters pronounced as 'alpha' and 'beta' respectively. We will use one more letter 'y' pronounced as 'gamma". |
Sum of zeroes for a quadratic polynomial ax²+bx+c
=a+b=-b/a=(coefficient of x)/coefficient of x²
Product of zeroes for a quadratic polynomial ax²+bx+c
=aß= c/a= constant term/coefficient of x²
Let us consider some examples.