Question

find a quadratic polynomial whose one zeros is5and product of its zero is 30

Answer 1

a=5
ab=30
5×b=30
b=30/5
b=6

a+b=5+6
a+b=11 (sum of zeroes)

ab=30 (product of zeroes)

x2-x(a+b)+(ab)=0
x2-11x+30=0
Hence the quadratic polynomial is-
x2-11x+30=0.

Answer 2

Answer: $x^{2} -11x +30$

Step-by-step explanation:

let first zero of the quadratic polynomial = a

second zero of the quadratic polynomial =b

Given:  a= 5  , ab= 30

$\Rightarrow b= \dfrac{30}{a} = \dfrac{30}5} =6$

Now

Sum of zeroes  = 6+5 = 11

Product of zeroes = 30

The quadratic polynomial is given by $x^{2} - Sx+ P$ where S is sum of zeroes and P is product of zeroes.

Therefore we get

$x^{2} -11x +30$

Hence, $x^{2} -11x +30$ is the required polynomial.