If 729 is divided by a natural number,quotient is 4 more than twice the divisor and reminder is 9 from the given information write the quadratic equation. also determine nature of its roots
Answers
Given : 729 is divided by a natural number quotient is 4 more than twice the divisor and reminder 9
To Find : write the quadratic equation
Solution:
a = bq + r
a= Dividend, b= Divisor, q= quotient and r = Remainder.
a = 729
r = 9
Let say b = x
quotient is 4 more than twice the divisor
=> q = 2x + 4
729 = x(2x + 4) + 9
=> 729 = 2x² + 4x + 9
=> 2x² + 4x + 9 - 729 = 0
=> 2x² + 4x - 720 = 0
=> x² + 2x - 360 = 0
=> x² + 20x - 18x - 360 = 0
=> x(x + 20) - 18(x + 20) = 0
=> (x - 18)(x + 20) = 0
=> x = 18 , x = -20
Discard the negative number
Roots are real & unequal
x² + 2x - 360 = 0 Quadratic Equation
Divisor = 18
Quotient = 40
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