Question

Find the zeroes of the quadratic polynomial x2-3x-4 and the verify the
relationship between the zeroes and the coefficient of the polynomial​

Answer 1

I do ur question plz check it

Answer 2

The zeros of the quadratic polynomial are x = -1 and x = 4

Solution:

Given that,

Given quadratic polynomial is:

$x^2- 3x - 4$

We have to find the zeros of the quadratic polynomial

From given,

$x^2- 3x - 4 = 0 \\\\Split\ the\ middle\ term \\\\x^2 + x - 4x - 4 = 0 \\\\\mathrm{Break\:the\:expression\:into\:groups} \\\\\left(x^2+x\right)+\left(-4x-4\right) = 0 \\\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+x\mathrm{:\quad }\\\\x(x+1) + (-4x-4) = 0 \\\\\mathrm{Factor\:out\:}-4\mathrm{\:from\:}-4x-4\\\\x\left(x+1\right)-4\left(x+1\right) = 0\\\\\mathrm{Factor\:out\:common\:term\:}x+1 \\\\\left(x+1\right)\left(x-4\right) = 0\\\\Thus\ the\ zeros\ are:\\\\x = -1\\\\x = 4$

Sum of zeros = -1 + 4 = 3

Product of zeros = - 1 x 4 = -4

The general quadratic equation is given as:

$x^2 - ( \text{ sum of zeros } )x + \text{ product of zeros } = 0$

Given is:

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

On comparing we get,

Sum of zeros = 3

Product of zeros = -4

Thus verified

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