Question

Find the quadratic polynomial whose are 1 and -3

Answer 1

The zeroes are 1 and - 3.

Sum = 1 - 3 = - 2.

Product = 1*-3 = - 3.

Required polynomial = k{x² - (sum) x + product}, where k≠0.

= k{x²+2x-3}, where k≠0.

Answer 2

Question

* Find the quadratic polynomial whose zeroes are 1 and -3

Solution

Method 1

Let the roots be α and β respectively

Given: α = 1 ; β = -3

We know that

Sum of the zeroes

=> α + β

=> 1 + (-3)

=> -2

Product of the zeroes

=> α × β

=> 1 × (-3)

=> -3

So, the polynomial = x² - (α + β) x + αβ = 0

=> x² - (-2) x + (-3) = 0

=> x² + 2x - 3 = 0

Method 2

Given:

x = 1 and x = -3 {roots of the equation}

=> (x - 1) (x + 3) = 0

=> x² + 3x - x - 3 = 0

=> x² + 2x - 3 = 0