Q. 364.5( 8 Votes )
Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
12abx2 – (9a2 – 8b2)x – 6ab = 0, where a ≠ 0 and b ≠ 0
Answer :
Given: 12abx2 – (9a2 – 8b2)x – 6ab = 0
Comparing with standard quadratic equation Ax2 + Bx + C = 0
A = 12ab, B = – (9a2 – 8b2), C = – 6ab
Discriminant D = B2 – 4AC
= [ – (9a2 – 8b2)]2 – 4.12ab. – 6ab
= 81a4 – 144a2b2 + 64b4 + 288 a2b2
= 81a4 + 144a2b2 + 64b4
= (9a2 + 8b2)2 > 0 Using a2 + 2ab + b2 = (a + b)2
Hence the roots of equation are real.
= 9a2 + 8b2
Roots 
are given by
Hence the roots of equation are 
Rate this question :
Get To Know About Quadratic Formula42 mins
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic EquationsFREE Class
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Quadratic Equation: Previous Year NTSE Questions32 mins
Champ Quiz | Quadratic Equation33 mins
Balance the Chemical Equations49 mins
Champ Quiz | Quadratic Equation48 mins
The sum of two numbers is 18 and the sum of their reciprocals is 
. Find the numbers.
Divide 12 into two parts such that their product is 32.
KC Sinha - MathematicsThe sum of the squares of three consecutive positive integers is 50. Find the integers.
KC Sinha - MathematicsThe difference of two numbers is 4. If the difference of their reciprocals is 
, find the two numbers.
The difference of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.
KC Sinha - MathematicsThe sum of a number and its reciprocal is 
. Find the number.
The difference of two numbers is 5 and the difference of their reciprocals is 
Find the numbers.
Divide 12 into two parts such that the sum of their squares is 74.
KC Sinha - MathematicsTwo numbers differ by 3 and their product is 504. Find the numbers.
KC Sinha - Mathematics