Question

What is the quadratic polynomial whose sum of zeros is -3/2 and the product of zeros is −1.

Answer 1

Solution :

Let the polynomial be ax²+bx+c ,

and it's zeroes be m and n.

Given m+n = -3/2 ,

mn = -1

We know that ,

the quadratic polynomial whose

zeroes m , n

= k[ x² - (m+n)x + mn ] where k € R

= k[ x² - (-3/2)x - 1 ]

= k [ x² + 3x/2 - 1 ]

If k = 2 , then the quadratic polynomial

is 2x² + 3x - 2

•••••

Answer 2

Given : Sum of zeroes of quadratic equation is -3/2 and product of zeroes is -1

To find : The quadratic equation

Solution :

A quadratic equation is an equation in which the highest degree of the variable is 2.

We are given the sum and product of zeroes of the quadratic equation and we have to find the equation.

To solve this problem, we should know a basic concept of a quadratic equation.

Every quadratic equation is of the form,

• x² - (sum)x + (Product)

Here,

• Sum = Sum of zeroes
• Product = Product of zeroes

Therefore, by substituting the values of sum and product of zeroes in the equation, we get :

⇒ x² - (-3/2)x - 1 = 0

⇒ x² + 3x/2 - 1 = 0

⇒ 2x² + 3x -2 = 0

Hence this is the required equation.

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