Question

Find the zeroes of the polynomial p ( x ) = √3x^2 + 10x + 7√3

Answer 1

√3x²+10x+7√3
√3x²+7x+3x+7√3
x(√3x+7)+√3(√3x+7)
(x+√3)(√3x+7)
x+√3=0 | √3x+7=0
x=-√3 | x= - 7/√3

Answer 2

If we want to get the zeroes of the polynomial, polynomial must be equal to 0.

Then,



= > √3 x² + 10 x + 7√3 = 0

= > √3 x² + ( 7 + 3 ) x + 7√3 = 0

= > √3 x² + 7x + 3x + 7√3 = 0

= > x( √3 x + 7 ) + √3( √3 x + 7 ) = 0

= > ( x + √3 ) ( √3 x + 7 ) = 0



$\: \: \: \: \: \: \: \: \: By \: Zero \: Product \: Rule , \:$



= > x = - √3


Or ,


= > √3 x = - 7

$= > x = - \frac{7}{ \sqrt{3} } \\ \\ \\ = > x = - \frac{7 \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } \\ \\ \\ = > x = - \frac{7 \sqrt{3} }{3}$






$Hence, \: Zeroes \: of \: the \: given \: polynomia l \: are \: \: - \frac{7 \sqrt{3} }{3} \: and \: - \sqrt{3}$