Question

Find the quadratic polynomial whose zeros are -3 and 4.

Answer 1

Hint: In this question use the concept that the zeros of the quadratic equation are the roots of the quadratic equation so use this property to reach the solution of the question.

Complete step-by-step answer:

As we know zeros are nothing but the roots of the polynomial.
So, it is given that the zeros of the quadratic polynomial are -3 and 4.
So the roots of the quadratic polynomial are -3 and 4.
Let the roots of the quadratic polynomial be $\alpha ,\beta $.
$ \Rightarrow \alpha = - 3{\text{ & }}\beta = 4$.
So, the quadratic equation satisfying these roots is,
$ \Rightarrow \left( {x - \alpha } \right)\left( {x - \beta } \right) = 0$
Now put the values of $\alpha ,\beta $ in this equation we have,
$ \Rightarrow \left( {x - \left( { - 3} \right)} \right)\left( {x - 4} \right) = 0$
Now simplify this equation we have,
$ \Rightarrow \left( {x + 3} \right)\left( {x - 4} \right) = 0$
$ \Rightarrow {x^2} - 4x + 3x - 12 = 0$
$ \Rightarrow {x^2} - x - 12 = 0$
So, this is the required quadratic polynomial having zeros -3 and 4.
So, this is the required answer.

Note: In such types of questions the key concept we have to remember is that zeros are the roots of the polynomial construct the quadratic equation satisfying these roots as above and simplify, we will get the required quadratic equation whose zeros is -3 and 4 which is the required answer.