Question

find the zeroes of the polynomial X2-9 and verify the relationship​

Answer 1

Answer:

MATHS

Find the zeros of the quadratic polynomial x2+9x+20, and verify the basic relationships between the zeros and the coefficients.

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ANSWER

Let p(x)=x2+9x+20=(x+4)(x+5)

So, p(x)=0→(x+4)(x+5)=0

∴x=−4 or x=−5

Thus, p(−4)=(−4+4)(−4+5)=0 and p(−5)=(−5+4)(−5+5)=0

Hence, the zeros of  ( ) p x  are -4 and -5 Thus,  sum of zeros = -9  and the product of zeros 20 =  (1) 

From the basic relationships, we get 

the sum of the zeros  =−cofficientx2coefficient of x=19=−9   (2)

product of the zeros =cofficientx2constantterm=120=20    (3)

Thus, the basic relationships are verified