Question

Show that 1 upon 2 and minus 3 upon 2 are zero of the polynomial 4 x square + 4 x minus 3 and also verify the relation between the zeros and coefficient of a polynomial

Answer 1

I hope it will help you

Answer 2

Step-by-step explanation:

Since we have given that

$\frac{1}{2}\ and\ \frac{-3}{2}$ are the zeroes of the polynomial i.e.

$4x^2+4x-3=0$

So, we will first factorise the above quadratic equation by "Split the middle term":

$4x^2+4x-3=0\\\\4x^2+6x-2x-3=0\\\\2x(2x+3)-1(2x+3)=0\\\\(2x-1)(2x+3)=0\\\\x=\frac{1}{2},\frac{-3}{2}$

So, we will verify the relation between the zeroes and coefficient of a polynomial.

Let α =$\frac{1}{2}$ , β = $\frac{-3}{2}$

And we know that

$\frac{1}{2}-\frac{3}{2}=\alpha +\beta =\frac{b}{a}=\frac{-4}{4}\\\\\frac{-2}{2}=\alpha +\beta =-1\\\\-1=\alpha +\beta -1$

Similarly,

$\frac{1}{2}\times \frac{-3}{2}=\alpha \beta =\frac{c}{a}=\frac{-3}{4}\\\\\frac{-3}{4}=\alpha \beta =\frac{-3}{4}$

Hence, verified.