Find फाइंड द जीरो ऑफ द फॉलोइंग कोडिंग पॉलिनॉमियल्स एंड वेरीफाई द रिलेशनशिप बिटवीन द जीरो एंड कॉफी एंड फर्स्ट एक्स स्क्वायर माइनस टू एक्स माइनस x2-2x-8
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10th
Maths
Polynomials
Relationship between Zeroes and Coefficients of a Polynomial
Find the zeros of the follo...
MATHS
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Asked on December 20, 2019 by
Anushma Balla
Find the zeros of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients:
x
2
−2x−8
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ANSWER
Given equation is x
2
−2x−8
x
2
−2x−8=x
2
−4x+2x−8
=x(x−4)+2(x−4)
=(x−4)(x+2)
The value of x
2
−2x−8 is zero when x−4=0 or x+2=0.
i.e, when x=4 or x=−2.
∴ The zeroes ofx
2
−2x−8 are 4 and −2.
sum of zeroes =4+(−2)=2
product of zeroes =−2×4=−8.
Relationship between the zeroes and the coefficients for the standard quadratic equation is ax
2
+bx+c=0
Sum of roots = −
a
b
and Product of roots =
a
c
In given equation
x
2
−2x−8=0
a=1,b=−2,c=−8
Sum of roots = −
1
−2
=2
and Product of roots =
1
−8
=−8
The relationship between the zeroes and the coefficients is verified.