Question

find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficient. (i)4xsquare-4x-3​

Answer 1

Answer :-

4x² - 4x - 3

Factorise it ;

4x² - 6x + 2x - 3

2x (2x - 3) + 1 (2x - 3)

(2x - 3) (2x + 1)

Now, 4x² - 4x - 3 = 0

(2x - 3) (2x + 1) = 0

=> 2x - 3 = 0

=> 2x = 3

=> x = $\dfrac{3}{2}$

Also, 2x + 1 = 0

=> 2x = -1

=> x = $\dfrac{-1}{2}$

So, $\dfrac{3}{2}$ & $\dfrac{-1}{2}$ are the zeroes of polynomial 4x² - 4x - 3.

Verification :-

Sum of zeroes = $\dfrac{3}{2}$ + $\dfrac{-1}{2}$ = $\dfrac{-b}{a}$

= $\dfrac{3 + (-1)}{2}$ = $\dfrac{-(-4)}{4}$

= $\dfrac{2}{2}$ = $\dfrac{4}{4}$

1 = 1

Also, Product of zeroes = $\dfrac{-1}{2}$ × $\dfrac{3}{2}$ = $\dfrac{c}{a}$

= $\dfrac{-3}{4}$ = $\dfrac{-3}{4}$

Hence, Verified ..!!