Question

y2 + 4root 3 y -15 and verify the realtionship between zeros​

Answer 1

Answer:

Analysis→

Here we're given an equation y²+4√3y-15 and we've to find the relation between the coefficients and the zeroes of the polynomial.So let the zeroes be α and β.And as it is a quadratic equation. So:-

$\mapsto\rm Sum\:of\:zeroes=\dfrac{-b}{a} \\ \rm and \\ \:\:\:\mapsto\rm Product\:of\:zeroes=\dfrac{c}{a}$

Given→

• Equation= y²+4√3y-15
• Coefficient of y (b)=4√3
• Coefficient of y² (a)=1
• Constant term (c)= -15

To Find→

Relation between coefficients and zeroes.

Answer→

$\Large\maltese{\underline{\underline{\rm{Sum\:of\:Zeroes\leadsto}}}}$

$\implies\rm{α+β=\dfrac{-b}{a}}$

$\implies\rm{α+β=\dfrac{-(4\sqrt{3})}{1}}$

$\implies\rm{α+β=-4\sqrt{3}}$

${\boxed{\boxed{\implies{\bold{α+β=-4\sqrt{3}}\checkmark}}}}$

$\Large\maltese{\underline{\underline{\rm{Product\:of\:Zeroes\leadsto}}}}$

$\implies\rm{αβ=\dfrac{c}{a}}$

$\implies\rm{αβ=\dfrac{-15}{1}}$

$\implies\rm{αβ=-15}$

${\boxed{\boxed{\implies{\bold{αβ=-15\checkmark}}}}}$

☞ Hence the sum of zeroes of the given polynomial is -4√3 and the product of zeroes is -15 which is the required answer.

HOPE IT HELPS.