Question

Find a quadratic is polynomial whose sum and product of the zeroes are -3/2√5 , -1/2
respectively Also find the zeros of the polynomial​

Answer 1

Answer:

equation

k[2√5x²+3x - √5 =0], where 'k' is a constant

zeros

4/6  or-10/6

Step-by-step explanation:

Given:

sum of polynomial = -3/2√5

product of zeros  = -1/2

Pre-requisite knowledge :

• Quadratic polynomial : A quadratic polynomial is a polynomial of degree 2.
• zeros of polynomial :Zeros (roots) of a function are the values of x for which f(x)=0
• Sum of the zeros of quadratic polynomial: $\alpha$+$\beta$=$\frac{-b}{a}$
• product of the zeroes :$\alpha$*$\beta$=$\frac{c}{a}$
• x2 − (sum of the roots)x + (product of the roots) = 0

Solution:

sum of polynomial = -3/2√5

$\alpha$+$\beta$=$\frac{-b}{a}$= -3/2√5

product of zeros  = -1/2

$\alpha$*$\beta$=$\frac{c}{a}$=-1/2

multiply √5 in both numerator and denominator

thus , it becomes = -√5/2√5

a= 2√5

    b = 3

  c = -√5

thus ,equation becomes

k[2√5x²+3x - √5 =0], where 'k' is a constant

to find zeros

quadratic equation

-b±√b²-4ac/2a

-3±√9 -4(2√5)(-√5)/2*3

or, -3±√49/6

or,-3±7/6

or,-3+7/6 =4/6  or

-3-7/6=-10/6

hence, equation

k[2√5x²+3x - √5 =0], where 'k' is a constant

zeros

4/6  or-10/6

*********************************