Question

If the mean of the zero of quadratic polynomial is 3 the sum of squares of them is 20 and it forms a rectangle find area of rectangle

Answer 1

Answer:

8

Step-by-step explanation:

Let x be one zero and y be the other zero of the polynomial

Given that:

(x+y)/2= 3

or

(x+y)=3*2=6

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2 \times x \times y \\ or \\ {(x + y)}^{2} - ( {x}^{2} + {y}^{2}) = 2 \times x \times y \\ ({(x + y)}^{2} - ( {x}^{2} + {y}^{2}) )\div 2 = x \times y$

x*y = area of the rectangle formed by x and y

Also given that:

${x}^{2} + {y}^{2} = 20$

Therefore

$area \: of \: the \: rectangle = x \times y = ({(x + y)}^{2} - ( {x}^{2} + {y}^{2}) )\div 2 \: \\ = ({6}^{2} - 20) \div 2 \\ = (36 - 20) \div 2 \\ = 16 \div 2 \\ = 8$

Area of the rectangle =8