Question

find a quadratic polynomial whose sum of zeros is -3/2root5 and the product of the zeroes is -1/2 also find the zeroes of the polynomial

Answer 1

Answer:

sum of zeroes is-3/2√5

product of zeroes is -1/2

equation of the quadratic polynomial is x² - ( sum of zeroes) + (product of zeroes)

=x²+ x(3/2√5) - 1/2 = 0

2√5 x² +3x -√5 =0

2√5x²+5x-2x-√5=0

√5x(2x+√5) -1(2x+√5)=0

(2x+√5)(√5x-1)=0

case1

2x+√5=0

2x= -√5

x=-√5/2

case2

√5x-1=0

√5x=1

x=1/√5

zeroes of the polynomial is 1/√5,-√5/2