Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and coefficients.

f(x) = x^2 - 4√3 - 15​

Answer 1

SOLUTION :

(x) Given : f(v) = x² + 4√3x -15

= x² - √3x + 5√3x - 15

= x(x - √3) + 5√3 (x - √3)

= (x - √3 ) (x + 5√3)

To find zeroes,  put f(x) = 0

(x - √3 )  = 0   or   (x + 5√3) = 0

x= √3  or  x = - 5√3

Hence, Zeroes of the polynomials are α = √3  and  β = -5√3

VERIFICATION :  

Sum of the zeroes = − coefficient of x / coefficient of x²

α + β = −coefficient of x / coefficient of x²

√3 +(-5√3)= - 4√3/1

- 4√3 = - 4√3

Product of the zeroes = constant term/ Coefficient of x²

α β = constant term / Coefficient of x²

√3 × -5√3 = -15/1

3 ×-5 = -15

-15 = -15

Hence, the relationship between the Zeroes and  its coefficients is verified.

Answer 2

Step-by-step explanation:

Solution is given in the above pic

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