Question

find the zeros of the quadratic polynomial 4√5x^2-24x-9√5 and verify its relationship between its zeroes and coefficients.........answer required urgently for my assignment

Answer 1

The zeros of the quadratic polynomial are

`x=(15√(5))/(10)` and
`x=-(3√(5))/(10)`

The relationship between its zeroes and coefficients in the procedure

Explanation:

step 1

Find the zeros

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`4√(5)x^(2)-24x-9√(5)=0`

so

`a=4√(5)\\b=-24\\c=-9√(5)`

substitute in the formula

`x=\frac{-(-24)(+/-)\sqrt{-24^(2)-4(4√(5))(-9√(5))}} {2(4√(5))}`

`x=\frac{24(+/-)\sqrt{-24^(2)-4(4√(5))(-9√(5))}} {8√(5)}`

`x=\frac{24(+/-)√(1,296)} {8√(5)}`

`x=\frac{24(+/-)36} {8√(5)}`

`x=\frac{24(+)36} {8√(5)}=(15√(5))/(10)`

`x=\frac{24(-)36} {8√(5)}=-(3√(5))/(10)`

step 2

Find the sum of the zeros and the product of the zeros

Sum of the zeros

`((15√(5))/(10))+(-(3√(5))/(10))=(12√(5))/(10)=(6√(5))/(5)`

Product of the zeros

`((15√(5))/(10))*(-(3√(5))/(10))=-(9)/(4)`

step 3

Verify that

Sum of the zeros= -Coefficient x/Coefficient x²

Coefficient x=-24

Coefficient x²=4√5

substitute

`(6√(5))/(5)=-(-24)/4√(5)\\ \\(6√(5))/(5)=(6√(5))/(5)`

therefore

the relationship is verified

step 4

Verify that

Product of the zeros= Constant term/Coefficient x²

Constant term=-9√5

Coefficient x²=4√5

substitute

`-(9)/(4)=(-9√(5))/4√(5)\\ \\-(9)/(4)=-(9)/(4)`

therefore

the relationship is verified