find the zeros of the polynomial x squared+3x-10 and verify the relation between its zeros and coefficient.
 

Asked by pritymishtu | 20th Jun, 2014, 09:32: PM

Expert Answer:

We have p(x) = x2+3x - 10 = (x + 5)(x - 2)
For any zero, p(x) = 0
rightwards double arrow x2+3x - 10 = 0
rightwards double arrow(x + 5)(x - 2) = 0
rightwards double arrow(x + 5) = 0 OR (x - 2) = 0
rightwards double arrowx = - 5 OR x = 2
The zeroes of p(x) = x2+3x - 10 are as alpha space equals space minus 5 space a n d space beta space equals space 2.
Now, sum of zeroes = alpha space plus space beta space equals space minus 5 space plus space 2 space equals space minus 3 space = minus space fraction numerator c o e f f i c i e n t space o f space x squared over denominator c o e f f i c i e n t space o f space x end fraction
Product of zeroes = alpha. beta space equals left parenthesis minus 5 right parenthesis left parenthesis 2 right parenthesis space space equals space minus 10 space equals space fraction numerator c o n s tan t space t e r m space over denominator c o e f f i c i e n t space o f space x squared end fraction

Answered by Mili Hariyani | 21st Jun, 2014, 09:49: AM

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