Question

Find the zeroes of the polynomial 2x²+4x and verify the relationship between the zeroes and their coefficients

Answer 1

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Answer 2

The given question is we have to find the zeroes of the

polynomial 2x²+4x and verify the relationship between the zeroes and their coefficients.

the zeroes of the polynomial is obtained by factorising the given polynomial

on factorising we get

$2 {x}^{2} + 4x = 0$

In the above expression the value of a= 2,b=4, c=0

on further proceeding we get

$2x(x + 2) = 0 \\ 2x = 0 \: and \: (x + 2) = 0 \\ x = 0 \: and \: x + 2 = 0 \\ x = - 2$

Where as the zeroes obtained was

$\alpha = 0 \\ \beta = - 2$

The sum and product of the zeroes are

$\alpha + \beta = 0 + ( -2 ) = - 2$

$\alpha \beta = (0) \times ( - 2) = 0$

The sum of zeroes obtained from the equation is

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

The product of zeroes obtained from the equation is

$\alpha \beta = \frac{c}{a} = \frac{0}{2} = 0$

Hence verified the relationship between zeroes and their coefficients

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