find the zeroes of the quadratic polynamial (4x2-4x-3) and verify the relation between its zeroes and coefficients - Maths - Polynomials

Question

find the zeroes of the quadratic polynamial
(4x2-4x-3) and verify the relation between its zeroes
and coefficients

Aakash Sharma · Accepted Answer

The given quadratic polynomial is

$4 x^{2} - 4 x - 3 = 4 x^{2} - 6 x + 2 x - 3 = 2 x (2 x - 3) + 1 (2 x - 3) = (2 x + 1) (2 x - 3)$

So the zeroes of the quadratic polynomial are

$- \frac{1}{2} and \frac{3}{2}$

$So, sum of zeroes = \frac{4}{4} \Rightarrow - \frac{1}{2} + \frac{3}{2} = 1 \Rightarrow \frac{2}{2} = 1 \Rightarrow 1 = 1 and product of zeroes = - \frac{3}{4} \Rightarrow - \frac{1}{2} \times \frac{3}{2} = - \frac{3}{4} \Rightarrow - \frac{3}{4} = - \frac{3}{4}$

find the zeroes of the quadratic polynamial (4x2-4x-3) and verify the relation between its zeroes and coefficients.

find the zeroes of the quadratic polynamial (4x²-4x-3) and verify the relation between its zeroes and coefficients.