Question

If a and b are the zeros of a polynomial x^2 – 3x – 4, then the polynomial whose zeroes are (a + b) and ab is​

Answer 1

Given,  

A polynomial  $x^{2} - 3x - 4$ with zeroes $a$ and $b$  

To find,  

Polynomial whose zeroes are $a + b$ and $ab$  

Solution,

Finding the roots of the given polynomial,

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

$x = -1, x = 4$ satisfy the given equation.

The value of $a = -1$ and $b = 4.$

For the new polynomial the roots will be,

  $\alpha = a +b = 3\\\beta = ab = -4$

The general form of quadratic equation using roots of the equation is,

                      $(x - p )(x - q) = 0$

Where $p$ and $q$ are the roots of the equation.

Substituting value of roots in the given general equation,

       $(x - 3)(x - (-4)) = 0\\(x - 3)(x + 4) = 0\\x^{2} + x -12 = 0$

Therefore, the new polynomial with the required zeroes is $x^{2} + x -12 = 0$.

Answer 2

Answer:

Step-by-step explanation:

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