3) Solve the following quadratic equation and give your answer correct to two significant figures: x+1/2x+5=x+3/3x+4
Answers
Step-by-step explanation:
(x+1)/(2x+5)=(x+3)/(3x+4)
(x+1)(3x+4)=(x+3)(2x+5)
3x^2+4x+3x+4=2x^2+5x+6x+15
3x^2+7x+4=2x^2+11x+15
3x^2-2x^2+7x-11x=15-4
x^2-4x=11
x^2-4x-11=0
a=1 ,b= -4 ,c=-11
roots= [-b(+-)√(b^2-4ac)]/2a
=[4(+-)√16-(4*-11)]/2
=[4(+-)√(16+44)]/2
=[4(+-)√60]/2
=[4+-√15*4]/2
=[4(+-)2√15]/2
=(4+2√15)/2. or. (4-2√15)/2
=2+√15. or. 2-√15
Given equation is
Its a quadratic in x and to solve this quadratic equation, we use Quadratic Formula, which is given by
Here,
So, on substituting the values, we get
Let evaluate now
So, on substituting the value, we get
Additional Information :-
Nature of roots :-
Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.
If Discriminant, D > 0, then roots of the equation are real and unequal.
If Discriminant, D = 0, then roots of the equation are real and equal.
If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.
Where,
Discriminant, D = b² - 4ac