A quadratic polynomial whose zeroes are 3/5 and -1/2, is (a) 10x^2 + x + 3

Question

A quadratic polynomial whose zeroes are \(\frac{3}5\) and \(\frac{-1}2\), is

(a) 10x² + x + 3 

(b) 10x² + x – 3 

(c) 10x² – x + 3 

(d) x² - \(\frac{1}{10}\)x - \(\frac{3}{10}\)

Answer 1

(d) x² - \(\frac{1}{10}\)x - \(\frac{3}{10}\) 

Here, the zeroes are \(\frac{3}5\) and \(\frac{-1}2\)

Let α = \(\frac{3}5\) and β = \(\frac{-1}2\)

So, sum of the zeroes, α + β = \(\frac{3}5\) + \((\frac{-1}2)\) = \(\frac{1}{10}\)

Also, product of the zeroes, αβ = \(\frac{3}5\) x \((\frac{-1}2)\) = \(\frac{-3}{10}\)

The polynomial will be x² – (α + β) x + αβ.

∴ The required polynomial is x² - \(\frac{1}{10}\)x - \(\frac{3}{10}\).