Question

Find the zeros of each of the following quadratic polynomial and verify the relationship between the zeros and their coefficients:
(x) $f(v)=v^{2} +4\sqrt{3v})-15$
(xi) $p(y)=y^{2}+\frac{3\sqrt{5}}{2}y-5$
(xii) $q(y)=7y^{2}-\frac{11}{3}y-\frac{2}{3}$

Answer 1

SOLUTION :

(x) Given : f(v) = v² + 4√3v -15

= v² - √3v + 5√3v - 15

= v(v - √3) + 5√3 (v - √3)

= (v - √3 ) (v + 5√3)

To find zeroes,  put f(v) = 0

(v - √3 )  = 0   or   (v + 5√3) = 0

v = √3  or  v = - 5√3

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

VERIFICATION :  

Sum of the zeroes = − coefficient of v / coefficient of v²

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 v²

α β = constant term / Coefficient of v²

√3 × -5√3 = -15/1

3 ×-5 = -15

-15 = -15

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

SOLUTIONS OF (xi) & (xii) ARE IN THE ATTACHMENT.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer of all three parts are in the above attachments....

Attachments are in this order like left to right

Slide the pages to see the answer of other parts...

HOPE THIS HELPS YOU...