Question

find the zeros of root 3 X square + 10 X + 7 root 3 and and relation between the zeros and coefficient​

Answer 1

GIVEN :

Equation : √3x² + 10x + 7√3

Finding the zeroes :

√3x² + 10x + 7√3

Split the middle term.

= √3x² + 7x + 3x + 7√3

= x(√3x + 7) + √3(√3x + 7)

= (x + √3) (√3x + 7) = 0

x = -√3 ; √3x = -7 , x = 7/√3

= -√3 and -7/√3

Zeroes are -√3 and -7/√3

Relation between zeroes and coefficients :

√3x² + 10x + 7√3

a = √3 ; b = 10 ; c = 7√3

Sum of zeroes :

α+β = (-√3) + (-7/√3)

= -√10/√3

= -b/a

= -10/√3

Product of zeroes :

αβ = 7√3 × √3

= 7√3/√3

= 7

= c/a

= 7√3/√3

= 7

Hence, Verified !!