determine the nature of the quadratic equation 9a^2b^2x^2 - 24abcdx + 16c^2d^2
Answers
EXPLANATION.
Quadratic equation.
⇒ 9a²b²x² - 24abcdx + 16c²d² = 0.
As we know that,
⇒ D = Discriminant Or b² - 4ac.
⇒ D = (-24abcd)² - 4(9a²b²)(16c²d²).
⇒ D = 576a²b²c²d² - 576a²b²c²d².
⇒ D = 0.
Nature of roots are real and equal : D = 0.
MORE INFORMATION.
Nature of roots of the quadratic expression.
(1) = Real and unequal, if b² - 4ac > 0.
(2) = Rational and different, if b² - 4ac is a perfect square.
(3) = Real and equal, if b² - 4ac = 0.
(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.
Dear Student,
• Given :
Quadratic Equation = 9a²2b²2x² - 24abcdx + 16c²2d²
• To Find :
To Determine the nature of the quadratic equation.
✪ Explanation :
➠ 9a²b²x² - 24abcdx + 16c²d² = 0
➠ Here,
A = 9a²b²x² , B = - 24abcd , C = 16c²d²
→ Use the Formula : B² - 4AC ←
➠ (−24abc) −4 ( 9a²b² ) (16c²d² )
➠ 576 a²b²c²d² - 576 a²b²c²d²
➠ 0
∴ Discriminant=0
⇒ Hence, roots of given quadratic equation are real and equal.