Quadratic equations which are expressed in the form of ax2

Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0. Someone writes, “Quadratic equations may have many solutions.” Is this statement correct? Explain why. 2. Choose one of the following two questions: (a) Write a word problem involving a quadratic function. How would you explain the steps in finding the solution to someone not in this class?

Solution

A quadratic equation ax^2 +bx+c=0 may have , 0, 1 or 2 solutions depending on the formula

b^2 -4ac

if b^2 -4ac <0 quadratic equation will have zero solution or we can say imaginary solutions.

if b^2 -4ac =0 , then there will be only 1 solution unique.

if b^2 -4ac >0 , there will be 2 solutions.

A rectangular farm of a farmer is 7200 square feet. The length of the farm is 10 feet longer than the width of the farm. FInd the dimensions.
Let width is x feet, the length is x+10.
x(x+10)=7200
x^2+10x-7200=0.
(x+90)(x-80)=0.
x=80. x=-90

x=-90 rejected cannot be negative

so

x=80

Hence width =80 ft and length =90 ft