Question

Find the zeroes of the polynomial 4x²-7x²-3 and verify the relationship between the zeroes and the coefficients​

Answer 1

Answer:

p( x )  = 4x² -7x - 3

= 4x² - 4x - 3x - 3  

= 4x ( x - 1 ) - 3 ( x + 1 )

(4x - 3 ) and ( x + 1 ) are its roots .

let zeroes be $\alpha$ and $\beta$ respectively .

4x- 3 = 0                                        =   x + 1 = 0  

= 4x = 3                                          = x = -  1

x = $\frac{3}{4}$

alpha + beta =  $\frac{3}{4}$ + 1 = $\frac{3+4}{4} = \frac{7}{4}$

alpha * beta = $\frac{3}{4}*-1 = \frac{-3}{4}$

$\frac{-b}{a} = \frac{-(-7)}{4} =\frac{7}{4}$

$\frac{c}{a} = \frac{-3}{4}$

As alpha + beta is equal to -b/a and alpha * beta = c/a            

Hence proved

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