Question

The quadratic polynomial, whose zeros are 3 and 4, is

Answer 1

The obtained polynomial is x^2+x-12x2+x−12having zeroes as 3 and -4.

To find:

Quadratic polynomial

Solution:

Given : Zeros of quadratic polynomial are 3 and -4.

Sum of zeros = 3 + (-4)  = -1

Product of zeros = (3)(-4) = -12

Now the required polynomial is  

\begin{gathered}\begin{array} { c } { x ^ { 2 } + ( \text {product of zeros} ) - x ( \text {sum of zeros} ) } \\\\ { = x ^ { 2 } + ( - 12 ) - x ( - 1 ) } \\\\ { = x ^ { 2 } - 12 + x } \\\\ { = x ^ { 2 } + x - 12 } \end{array}\end{gathered}x2+(product of zeros)−x(sum of zeros)=x2+(−12)−x(−1)=x2−12+x=x2+x−12

Thus, the obtained polynomial is x^2+x-12x2+x−12 having zeroes as 3 and -4.

hope you will understand